Abstract

Quantum mechanics allows measurements that surpass the fundamental sensitivity limits of classical methods. To benefit from the quantum advantage in a practical setting, the receiver should use communication channel resources optimally; this can be done employing large communication alphabets. Here we show the fundamental sensitivity potential of a quantum receiver for coherent communication with frequency shift keying. We introduce an adaptive quantum protocol for this receiver and show that its sensitivity outperforms other receivers for alphabet sizes above 4 and scales favorably, whereas quantum receivers explored to date suffer from degraded sensitivity with the alphabet size. In addition, we show that the quantum measurement advantage allows much better use of the frequency space in comparison to classical frequency keying protocols and orthogonal frequency division multiplexing.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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  1. Homer, “The Iliad,” (Book XVIII, Lines 200–213, VIII–VII B.C.), http://www.perseus.tufts.edu/hopper/text?doc=urn:cts:greekLit:tlg0012.tlg001.perseus-eng1:18.181-18.218 .
  2. R. Maher, A. Alvarado, D. Lavery, and P. Bayvel, “Increasing the information rates of optical communications via coded modulation: a study of transceiver performance,” Sci. Rep. 6, 21278 (2016).
    [Crossref]
  3. M. Armbrust, A. Fox, R. Griffith, A. D. Joseph, R. Katz, A. Konwinski, G. Lee, D. Patterson, A. Rabkin, I. Stoica, and M. Zaharia, “A view of cloud computing,” Commun. ACM 53, 50–58 (2010).
    [Crossref]
  4. A. Mecozzi, C. Antonelli, and M. Shtaif, “Kramers–Kronig coherent receiver,” Optica 3, 1220–1227 (2016).
    [Crossref]
  5. P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546, 274–279 (2017).
    [Crossref]
  6. N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
    [Crossref]
  7. D. Millar, R. Maher, D. Lavery, T. Koike-Akino, A. Alvarado, M. Paskov, K. Kojima, K. Parsons, B. C. Thomsen, S. J. Savory, and P. Bayvel, “Transceiver-limited high spectral efficiency Nyquist-WDM systems,” in Optical Fiber Communication Conference (Optical Society of America, 2015), paper Th2A.13.
  8. R. Maher, D. Lavery, D. Millar, A. Alvarado, K. Parsons, R. Killey, and P. Bayvel, “Reach enhancement of 100% for a DP-64 QAM super-channel using MC-DBP,” in Optical Fiber Communication Conference (Optical Society of America, 2015), paper Th4D.5.
  9. S. Cherry, “Edholm’s law of bandwidth,” IEEE Spectrum 41, 58–60 (2004).
    [Crossref]
  10. E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).
    [Crossref]
  11. R. J. Cesarone, D. S. Abraham, S. Shambayati, and J. Rush, “Deep-space optical communications,” in International Conference on Space Optical Systems and Applications (ICSOS) (2011), pp. 410–423.
  12. H. Kaushal and G. Kaddoum, “Optical communication in space: challenges and mitigation techniques,” IEEE Commun. Surv. Tutorials 19, 57–96 (2017).
    [Crossref]
  13. J. Proakis, Digital Communications, Electrical Engineering Series (McGraw-Hill, 2001).
  14. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
  15. H. P. Robertson, “The uncertainty principle,” Phys. Rev. 34, 163–164 (1929).
    [Crossref]
  16. C. M. Caves, “Quantum-mechanical radiation-pressure fluctuations in an interferometer,” Phys. Rev. Lett. 45, 75–79 (1980).
    [Crossref]
  17. C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23, 1693–1708 (1981).
    [Crossref]
  18. K. Kikuchi and S. Tsukamoto, “Evaluation of sensitivity of the digital coherent receiver,” J. Lightwave Technol. 26, 1817–1822 (2008).
    [Crossref]
  19. S. L. Braunstein and H. J. Kimble, “Dense coding for continuous variables,” Phys. Rev. A 61, 042302 (2000).
    [Crossref]
  20. P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
    [Crossref]
  21. M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7, 229–233 (2013).
    [Crossref]
  22. C. W. Helstrom, “Quantum detection and estimation theory,” J. Stat. Phys. 1, 231–252 (1969).
    [Crossref]
  23. K. Tsujino, D. Fukuda, G. Fujii, S. Inoue, M. Fujiwara, M. Takeoka, and M. Sasaki, “Sub-shot-noise-limit discrimination of on-off keyed coherent signals via a quantum receiver with a superconducting transition edge sensor,” Opt. Express 18, 8107–8114 (2010).
    [Crossref]
  24. K. Tsujino, D. Fukuda, G. Fujii, S. Inoue, M. Fujiwara, M. Takeoka, and M. Sasaki, “Quantum receiver beyond the standard quantum limit of coherent optical communication,” Phys. Rev. Lett. 106, 250503 (2011).
    [Crossref]
  25. Y. Koizumi, K. Toyoda, M. Yoshida, and M. Nakazawa, “1024 QAM (60  Gbit/s) single-carrier coherent optical transmission over 150  km,” Opt. Express 20, 12508–12514 (2012).
    [Crossref]
  26. Q. Chen, J. He, R. Deng, M. Chen, and L. Chen, “FFT-size efficient 4096-QAM OFDM for low-cost DML-based IMDD system,” IEEE Photon. J. 8, 7804010 (2016).
    [Crossref]
  27. F. E. Becerra, J. Fan, G. Baumgartner, S. V. Polyakov, J. Goldhar, J. T. Kosloski, and A. Migdall, “M-ary-state phase-shift-keying discrimination below the homodyne limit,” Phys. Rev. A 84, 062324 (2011).
    [Crossref]
  28. C. R. Müller and C. Marquardt, “A robust quantum receiver for phase shift keyed signals,” New J. Phys. 17, 032003 (2015).
    [Crossref]
  29. Y. Zuo, K. Li, and B. Zhu, “16-QAM quantum receiver with hybrid structure outperforming the standard quantum limit,” MATEC Web Conf. 61, 06008 (2016).
    [Crossref]
  30. F. Becerra, J. Fan, G. Baumgartner, J. Goldhar, J. Kosloski, and A. Migdall, “Experimental demonstration of a receiver beating the standard quantum limit for multiple nonorthogonal state discrimination,” Nat. Photonics 7, 147–152 (2013).
    [Crossref]
  31. F. Becerra, J. Fan, and A. Migdall, “Photon number resolution enables quantum receiver for realistic coherent optical communications,” Nat. Photonics 9, 48–53 (2015).
    [Crossref]
  32. S. Guha, J. L. Habif, and M. Takeoka, “Approaching Helstrom limits to optical pulse-position demodulation using single photon detection and optical feedback,” J. Mod. Opt. 58, 257–265 (2011).
    [Crossref]
  33. S. J. Dolinar, “Quantum limits in interferometric measurements,” Technical Report (Research Laboratory of Electronics, MIT, 1973).
  34. R. S. Kennedy, “Quantum limits in interferometric measurements,” Technical Report (Research Laboratory of Electronics, MIT, 1972).
  35. M. T. Jaekel and S. Reynaud, “Quantum limits in interferometric measurements,” Europhys. Lett. 13, 301–306 (1990).
    [Crossref]
  36. V. P. Belavkin, “Optimum distinction of non-orthogonal quantum signals,” Radiotekhnika i Elektronika 20, 1177–1185 (1975).
  37. A. S. Holevo, “On capacity of a quantum communications channel,” Probl. Peredachi Inform. 15, 3–11 (1979).
  38. P. Hausladen, R. Jozsa, B. Schumacher, M. Westmoreland, and W. K. Wootters, “Classical information capacity of a quantum channel,” Phys. Rev. A 54, 1869–1876 (1996).
    [Crossref]
  39. K. Kato, M. Osaki, M. Sasaki, and O. Hirota, “Quantum detection and mutual information for QAM and PSK signals,” IEEE Trans. Commun. 47, 248–254 (1999).
    [Crossref]
  40. S. Ross, Introduction to Probability Models (Academic, 2007).
  41. A. Goun, D. I. Bondar, A. O. Er, Z. Quine, and H. A. Rabitz, “Photonic reagents for concentration measurement of fluorescent proteins with overlapping spectra,” Sci. Rep. 6, 25827 (2016).
    [Crossref]
  42. T. Kawanishi, T. Sakamoto, T. Miyazaki, M. Izutsu, T. Fujita, S. Mori, K. Higuma, and J. Ichikawa, “High-speed optical DQPSK and FSK modulation using integrated Mach–Zehnder interferometers,” Opt. Express 14, 4469–4478 (2006).
    [Crossref]

2017 (2)

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546, 274–279 (2017).
[Crossref]

H. Kaushal and G. Kaddoum, “Optical communication in space: challenges and mitigation techniques,” IEEE Commun. Surv. Tutorials 19, 57–96 (2017).
[Crossref]

2016 (6)

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).
[Crossref]

R. Maher, A. Alvarado, D. Lavery, and P. Bayvel, “Increasing the information rates of optical communications via coded modulation: a study of transceiver performance,” Sci. Rep. 6, 21278 (2016).
[Crossref]

Q. Chen, J. He, R. Deng, M. Chen, and L. Chen, “FFT-size efficient 4096-QAM OFDM for low-cost DML-based IMDD system,” IEEE Photon. J. 8, 7804010 (2016).
[Crossref]

Y. Zuo, K. Li, and B. Zhu, “16-QAM quantum receiver with hybrid structure outperforming the standard quantum limit,” MATEC Web Conf. 61, 06008 (2016).
[Crossref]

A. Goun, D. I. Bondar, A. O. Er, Z. Quine, and H. A. Rabitz, “Photonic reagents for concentration measurement of fluorescent proteins with overlapping spectra,” Sci. Rep. 6, 25827 (2016).
[Crossref]

A. Mecozzi, C. Antonelli, and M. Shtaif, “Kramers–Kronig coherent receiver,” Optica 3, 1220–1227 (2016).
[Crossref]

2015 (2)

C. R. Müller and C. Marquardt, “A robust quantum receiver for phase shift keyed signals,” New J. Phys. 17, 032003 (2015).
[Crossref]

F. Becerra, J. Fan, and A. Migdall, “Photon number resolution enables quantum receiver for realistic coherent optical communications,” Nat. Photonics 9, 48–53 (2015).
[Crossref]

2013 (3)

F. Becerra, J. Fan, G. Baumgartner, J. Goldhar, J. Kosloski, and A. Migdall, “Experimental demonstration of a receiver beating the standard quantum limit for multiple nonorthogonal state discrimination,” Nat. Photonics 7, 147–152 (2013).
[Crossref]

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7, 229–233 (2013).
[Crossref]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref]

2012 (1)

2011 (3)

S. Guha, J. L. Habif, and M. Takeoka, “Approaching Helstrom limits to optical pulse-position demodulation using single photon detection and optical feedback,” J. Mod. Opt. 58, 257–265 (2011).
[Crossref]

F. E. Becerra, J. Fan, G. Baumgartner, S. V. Polyakov, J. Goldhar, J. T. Kosloski, and A. Migdall, “M-ary-state phase-shift-keying discrimination below the homodyne limit,” Phys. Rev. A 84, 062324 (2011).
[Crossref]

K. Tsujino, D. Fukuda, G. Fujii, S. Inoue, M. Fujiwara, M. Takeoka, and M. Sasaki, “Quantum receiver beyond the standard quantum limit of coherent optical communication,” Phys. Rev. Lett. 106, 250503 (2011).
[Crossref]

2010 (2)

M. Armbrust, A. Fox, R. Griffith, A. D. Joseph, R. Katz, A. Konwinski, G. Lee, D. Patterson, A. Rabkin, I. Stoica, and M. Zaharia, “A view of cloud computing,” Commun. ACM 53, 50–58 (2010).
[Crossref]

K. Tsujino, D. Fukuda, G. Fujii, S. Inoue, M. Fujiwara, M. Takeoka, and M. Sasaki, “Sub-shot-noise-limit discrimination of on-off keyed coherent signals via a quantum receiver with a superconducting transition edge sensor,” Opt. Express 18, 8107–8114 (2010).
[Crossref]

2008 (1)

2006 (1)

2005 (1)

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
[Crossref]

2004 (1)

S. Cherry, “Edholm’s law of bandwidth,” IEEE Spectrum 41, 58–60 (2004).
[Crossref]

2000 (1)

S. L. Braunstein and H. J. Kimble, “Dense coding for continuous variables,” Phys. Rev. A 61, 042302 (2000).
[Crossref]

1999 (1)

K. Kato, M. Osaki, M. Sasaki, and O. Hirota, “Quantum detection and mutual information for QAM and PSK signals,” IEEE Trans. Commun. 47, 248–254 (1999).
[Crossref]

1996 (1)

P. Hausladen, R. Jozsa, B. Schumacher, M. Westmoreland, and W. K. Wootters, “Classical information capacity of a quantum channel,” Phys. Rev. A 54, 1869–1876 (1996).
[Crossref]

1990 (1)

M. T. Jaekel and S. Reynaud, “Quantum limits in interferometric measurements,” Europhys. Lett. 13, 301–306 (1990).
[Crossref]

1981 (1)

C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23, 1693–1708 (1981).
[Crossref]

1980 (1)

C. M. Caves, “Quantum-mechanical radiation-pressure fluctuations in an interferometer,” Phys. Rev. Lett. 45, 75–79 (1980).
[Crossref]

1979 (1)

A. S. Holevo, “On capacity of a quantum communications channel,” Probl. Peredachi Inform. 15, 3–11 (1979).

1975 (1)

V. P. Belavkin, “Optimum distinction of non-orthogonal quantum signals,” Radiotekhnika i Elektronika 20, 1177–1185 (1975).

1969 (1)

C. W. Helstrom, “Quantum detection and estimation theory,” J. Stat. Phys. 1, 231–252 (1969).
[Crossref]

1929 (1)

H. P. Robertson, “The uncertainty principle,” Phys. Rev. 34, 163–164 (1929).
[Crossref]

Abraham, D. S.

R. J. Cesarone, D. S. Abraham, S. Shambayati, and J. Rush, “Deep-space optical communications,” in International Conference on Space Optical Systems and Applications (ICSOS) (2011), pp. 410–423.

Agrell, E.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).
[Crossref]

Alvarado, A.

R. Maher, A. Alvarado, D. Lavery, and P. Bayvel, “Increasing the information rates of optical communications via coded modulation: a study of transceiver performance,” Sci. Rep. 6, 21278 (2016).
[Crossref]

R. Maher, D. Lavery, D. Millar, A. Alvarado, K. Parsons, R. Killey, and P. Bayvel, “Reach enhancement of 100% for a DP-64 QAM super-channel using MC-DBP,” in Optical Fiber Communication Conference (Optical Society of America, 2015), paper Th4D.5.

D. Millar, R. Maher, D. Lavery, T. Koike-Akino, A. Alvarado, M. Paskov, K. Kojima, K. Parsons, B. C. Thomsen, S. J. Savory, and P. Bayvel, “Transceiver-limited high spectral efficiency Nyquist-WDM systems,” in Optical Fiber Communication Conference (Optical Society of America, 2015), paper Th2A.13.

Anderson, M. H.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546, 274–279 (2017).
[Crossref]

Antonelli, C.

Armbrust, M.

M. Armbrust, A. Fox, R. Griffith, A. D. Joseph, R. Katz, A. Konwinski, G. Lee, D. Patterson, A. Rabkin, I. Stoica, and M. Zaharia, “A view of cloud computing,” Commun. ACM 53, 50–58 (2010).
[Crossref]

Bachor, H.-A.

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7, 229–233 (2013).
[Crossref]

Baumgartner, G.

F. Becerra, J. Fan, G. Baumgartner, J. Goldhar, J. Kosloski, and A. Migdall, “Experimental demonstration of a receiver beating the standard quantum limit for multiple nonorthogonal state discrimination,” Nat. Photonics 7, 147–152 (2013).
[Crossref]

F. E. Becerra, J. Fan, G. Baumgartner, S. V. Polyakov, J. Goldhar, J. T. Kosloski, and A. Migdall, “M-ary-state phase-shift-keying discrimination below the homodyne limit,” Phys. Rev. A 84, 062324 (2011).
[Crossref]

Bayvel, P.

R. Maher, A. Alvarado, D. Lavery, and P. Bayvel, “Increasing the information rates of optical communications via coded modulation: a study of transceiver performance,” Sci. Rep. 6, 21278 (2016).
[Crossref]

D. Millar, R. Maher, D. Lavery, T. Koike-Akino, A. Alvarado, M. Paskov, K. Kojima, K. Parsons, B. C. Thomsen, S. J. Savory, and P. Bayvel, “Transceiver-limited high spectral efficiency Nyquist-WDM systems,” in Optical Fiber Communication Conference (Optical Society of America, 2015), paper Th2A.13.

R. Maher, D. Lavery, D. Millar, A. Alvarado, K. Parsons, R. Killey, and P. Bayvel, “Reach enhancement of 100% for a DP-64 QAM super-channel using MC-DBP,” in Optical Fiber Communication Conference (Optical Society of America, 2015), paper Th4D.5.

Becerra, F.

F. Becerra, J. Fan, and A. Migdall, “Photon number resolution enables quantum receiver for realistic coherent optical communications,” Nat. Photonics 9, 48–53 (2015).
[Crossref]

F. Becerra, J. Fan, G. Baumgartner, J. Goldhar, J. Kosloski, and A. Migdall, “Experimental demonstration of a receiver beating the standard quantum limit for multiple nonorthogonal state discrimination,” Nat. Photonics 7, 147–152 (2013).
[Crossref]

Becerra, F. E.

F. E. Becerra, J. Fan, G. Baumgartner, S. V. Polyakov, J. Goldhar, J. T. Kosloski, and A. Migdall, “M-ary-state phase-shift-keying discrimination below the homodyne limit,” Phys. Rev. A 84, 062324 (2011).
[Crossref]

Belavkin, V. P.

V. P. Belavkin, “Optimum distinction of non-orthogonal quantum signals,” Radiotekhnika i Elektronika 20, 1177–1185 (1975).

Beth, T.

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
[Crossref]

Binosi, D.

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
[Crossref]

Blatt, R.

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
[Crossref]

Bondar, D. I.

A. Goun, D. I. Bondar, A. O. Er, Z. Quine, and H. A. Rabitz, “Photonic reagents for concentration measurement of fluorescent proteins with overlapping spectra,” Sci. Rep. 6, 25827 (2016).
[Crossref]

Bowen, W. P.

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7, 229–233 (2013).
[Crossref]

Bowers, J. E.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).
[Crossref]

Bozinovic, N.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref]

Brandt-Pearce, M.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).
[Crossref]

Brasch, V.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546, 274–279 (2017).
[Crossref]

Braunstein, S. L.

S. L. Braunstein and H. J. Kimble, “Dense coding for continuous variables,” Phys. Rev. A 61, 042302 (2000).
[Crossref]

Briegel, H.

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
[Crossref]

Bruss, D.

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
[Crossref]

Calarco, T.

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
[Crossref]

Caves, C. M.

C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23, 1693–1708 (1981).
[Crossref]

C. M. Caves, “Quantum-mechanical radiation-pressure fluctuations in an interferometer,” Phys. Rev. Lett. 45, 75–79 (1980).
[Crossref]

Cesarone, R. J.

R. J. Cesarone, D. S. Abraham, S. Shambayati, and J. Rush, “Deep-space optical communications,” in International Conference on Space Optical Systems and Applications (ICSOS) (2011), pp. 410–423.

Chen, L.

Q. Chen, J. He, R. Deng, M. Chen, and L. Chen, “FFT-size efficient 4096-QAM OFDM for low-cost DML-based IMDD system,” IEEE Photon. J. 8, 7804010 (2016).
[Crossref]

Chen, M.

Q. Chen, J. He, R. Deng, M. Chen, and L. Chen, “FFT-size efficient 4096-QAM OFDM for low-cost DML-based IMDD system,” IEEE Photon. J. 8, 7804010 (2016).
[Crossref]

Chen, Q.

Q. Chen, J. He, R. Deng, M. Chen, and L. Chen, “FFT-size efficient 4096-QAM OFDM for low-cost DML-based IMDD system,” IEEE Photon. J. 8, 7804010 (2016).
[Crossref]

Cherry, S.

S. Cherry, “Edholm’s law of bandwidth,” IEEE Spectrum 41, 58–60 (2004).
[Crossref]

Chraplyvy, A. R.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).
[Crossref]

Cirac, J. I.

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
[Crossref]

Daria, V.

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7, 229–233 (2013).
[Crossref]

Deng, R.

Q. Chen, J. He, R. Deng, M. Chen, and L. Chen, “FFT-size efficient 4096-QAM OFDM for low-cost DML-based IMDD system,” IEEE Photon. J. 8, 7804010 (2016).
[Crossref]

Deutsch, D.

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
[Crossref]

Dolinar, S. J.

S. J. Dolinar, “Quantum limits in interferometric measurements,” Technical Report (Research Laboratory of Electronics, MIT, 1973).

Eggleton, B. J.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).
[Crossref]

Eisert, J.

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
[Crossref]

Ekert, A.

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
[Crossref]

Er, A. O.

A. Goun, D. I. Bondar, A. O. Er, Z. Quine, and H. A. Rabitz, “Photonic reagents for concentration measurement of fluorescent proteins with overlapping spectra,” Sci. Rep. 6, 25827 (2016).
[Crossref]

Fabre, C.

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
[Crossref]

Fan, J.

F. Becerra, J. Fan, and A. Migdall, “Photon number resolution enables quantum receiver for realistic coherent optical communications,” Nat. Photonics 9, 48–53 (2015).
[Crossref]

F. Becerra, J. Fan, G. Baumgartner, J. Goldhar, J. Kosloski, and A. Migdall, “Experimental demonstration of a receiver beating the standard quantum limit for multiple nonorthogonal state discrimination,” Nat. Photonics 7, 147–152 (2013).
[Crossref]

F. E. Becerra, J. Fan, G. Baumgartner, S. V. Polyakov, J. Goldhar, J. T. Kosloski, and A. Migdall, “M-ary-state phase-shift-keying discrimination below the homodyne limit,” Phys. Rev. A 84, 062324 (2011).
[Crossref]

Fischer, J. K.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).
[Crossref]

Fox, A.

M. Armbrust, A. Fox, R. Griffith, A. D. Joseph, R. Katz, A. Konwinski, G. Lee, D. Patterson, A. Rabkin, I. Stoica, and M. Zaharia, “A view of cloud computing,” Commun. ACM 53, 50–58 (2010).
[Crossref]

Freude, W.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546, 274–279 (2017).
[Crossref]

Fujii, G.

K. Tsujino, D. Fukuda, G. Fujii, S. Inoue, M. Fujiwara, M. Takeoka, and M. Sasaki, “Quantum receiver beyond the standard quantum limit of coherent optical communication,” Phys. Rev. Lett. 106, 250503 (2011).
[Crossref]

K. Tsujino, D. Fukuda, G. Fujii, S. Inoue, M. Fujiwara, M. Takeoka, and M. Sasaki, “Sub-shot-noise-limit discrimination of on-off keyed coherent signals via a quantum receiver with a superconducting transition edge sensor,” Opt. Express 18, 8107–8114 (2010).
[Crossref]

Fujita, T.

Fujiwara, M.

K. Tsujino, D. Fukuda, G. Fujii, S. Inoue, M. Fujiwara, M. Takeoka, and M. Sasaki, “Quantum receiver beyond the standard quantum limit of coherent optical communication,” Phys. Rev. Lett. 106, 250503 (2011).
[Crossref]

K. Tsujino, D. Fukuda, G. Fujii, S. Inoue, M. Fujiwara, M. Takeoka, and M. Sasaki, “Sub-shot-noise-limit discrimination of on-off keyed coherent signals via a quantum receiver with a superconducting transition edge sensor,” Opt. Express 18, 8107–8114 (2010).
[Crossref]

Fukuda, D.

K. Tsujino, D. Fukuda, G. Fujii, S. Inoue, M. Fujiwara, M. Takeoka, and M. Sasaki, “Quantum receiver beyond the standard quantum limit of coherent optical communication,” Phys. Rev. Lett. 106, 250503 (2011).
[Crossref]

K. Tsujino, D. Fukuda, G. Fujii, S. Inoue, M. Fujiwara, M. Takeoka, and M. Sasaki, “Sub-shot-noise-limit discrimination of on-off keyed coherent signals via a quantum receiver with a superconducting transition edge sensor,” Opt. Express 18, 8107–8114 (2010).
[Crossref]

Gisin, N.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).
[Crossref]

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
[Crossref]

Goldhar, J.

F. Becerra, J. Fan, G. Baumgartner, J. Goldhar, J. Kosloski, and A. Migdall, “Experimental demonstration of a receiver beating the standard quantum limit for multiple nonorthogonal state discrimination,” Nat. Photonics 7, 147–152 (2013).
[Crossref]

F. E. Becerra, J. Fan, G. Baumgartner, S. V. Polyakov, J. Goldhar, J. T. Kosloski, and A. Migdall, “M-ary-state phase-shift-keying discrimination below the homodyne limit,” Phys. Rev. A 84, 062324 (2011).
[Crossref]

Goun, A.

A. Goun, D. I. Bondar, A. O. Er, Z. Quine, and H. A. Rabitz, “Photonic reagents for concentration measurement of fluorescent proteins with overlapping spectra,” Sci. Rep. 6, 25827 (2016).
[Crossref]

Grangiere, P.

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
[Crossref]

Grassl, M.

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
[Crossref]

Griffith, R.

M. Armbrust, A. Fox, R. Griffith, A. D. Joseph, R. Katz, A. Konwinski, G. Lee, D. Patterson, A. Rabkin, I. Stoica, and M. Zaharia, “A view of cloud computing,” Commun. ACM 53, 50–58 (2010).
[Crossref]

Guha, S.

S. Guha, J. L. Habif, and M. Takeoka, “Approaching Helstrom limits to optical pulse-position demodulation using single photon detection and optical feedback,” J. Mod. Opt. 58, 257–265 (2011).
[Crossref]

Habif, J. L.

S. Guha, J. L. Habif, and M. Takeoka, “Approaching Helstrom limits to optical pulse-position demodulation using single photon detection and optical feedback,” J. Mod. Opt. 58, 257–265 (2011).
[Crossref]

Hage, B.

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7, 229–233 (2013).
[Crossref]

Haroche, S.

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
[Crossref]

Hausladen, P.

P. Hausladen, R. Jozsa, B. Schumacher, M. Westmoreland, and W. K. Wootters, “Classical information capacity of a quantum channel,” Phys. Rev. A 54, 1869–1876 (1996).
[Crossref]

He, J.

Q. Chen, J. He, R. Deng, M. Chen, and L. Chen, “FFT-size efficient 4096-QAM OFDM for low-cost DML-based IMDD system,” IEEE Photon. J. 8, 7804010 (2016).
[Crossref]

Helstrom, C. W.

C. W. Helstrom, “Quantum detection and estimation theory,” J. Stat. Phys. 1, 231–252 (1969).
[Crossref]

Higuma, K.

Hirota, O.

K. Kato, M. Osaki, M. Sasaki, and O. Hirota, “Quantum detection and mutual information for QAM and PSK signals,” IEEE Trans. Commun. 47, 248–254 (1999).
[Crossref]

Holevo, A. S.

A. S. Holevo, “On capacity of a quantum communications channel,” Probl. Peredachi Inform. 15, 3–11 (1979).

Huang, H.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref]

Ichikawa, J.

Imamoglu, A.

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
[Crossref]

Inoue, S.

K. Tsujino, D. Fukuda, G. Fujii, S. Inoue, M. Fujiwara, M. Takeoka, and M. Sasaki, “Quantum receiver beyond the standard quantum limit of coherent optical communication,” Phys. Rev. Lett. 106, 250503 (2011).
[Crossref]

K. Tsujino, D. Fukuda, G. Fujii, S. Inoue, M. Fujiwara, M. Takeoka, and M. Sasaki, “Sub-shot-noise-limit discrimination of on-off keyed coherent signals via a quantum receiver with a superconducting transition edge sensor,” Opt. Express 18, 8107–8114 (2010).
[Crossref]

Izutsu, M.

Jaekel, M. T.

M. T. Jaekel and S. Reynaud, “Quantum limits in interferometric measurements,” Europhys. Lett. 13, 301–306 (1990).
[Crossref]

Janousek, J.

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7, 229–233 (2013).
[Crossref]

Joseph, A. D.

M. Armbrust, A. Fox, R. Griffith, A. D. Joseph, R. Katz, A. Konwinski, G. Lee, D. Patterson, A. Rabkin, I. Stoica, and M. Zaharia, “A view of cloud computing,” Commun. ACM 53, 50–58 (2010).
[Crossref]

Jozsa, R.

P. Hausladen, R. Jozsa, B. Schumacher, M. Westmoreland, and W. K. Wootters, “Classical information capacity of a quantum channel,” Phys. Rev. A 54, 1869–1876 (1996).
[Crossref]

Kaddoum, G.

H. Kaushal and G. Kaddoum, “Optical communication in space: challenges and mitigation techniques,” IEEE Commun. Surv. Tutorials 19, 57–96 (2017).
[Crossref]

Karlson, A.

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
[Crossref]

Karlsson, M.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).
[Crossref]

Karpov, M.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546, 274–279 (2017).
[Crossref]

Kato, K.

K. Kato, M. Osaki, M. Sasaki, and O. Hirota, “Quantum detection and mutual information for QAM and PSK signals,” IEEE Trans. Commun. 47, 248–254 (1999).
[Crossref]

Katz, R.

M. Armbrust, A. Fox, R. Griffith, A. D. Joseph, R. Katz, A. Konwinski, G. Lee, D. Patterson, A. Rabkin, I. Stoica, and M. Zaharia, “A view of cloud computing,” Commun. ACM 53, 50–58 (2010).
[Crossref]

Kaushal, H.

H. Kaushal and G. Kaddoum, “Optical communication in space: challenges and mitigation techniques,” IEEE Commun. Surv. Tutorials 19, 57–96 (2017).
[Crossref]

Kawanishi, T.

Kemal, J. N.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546, 274–279 (2017).
[Crossref]

Kempe, J.

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
[Crossref]

Kennedy, R. S.

R. S. Kennedy, “Quantum limits in interferometric measurements,” Technical Report (Research Laboratory of Electronics, MIT, 1972).

Kikuchi, K.

Killey, R.

R. Maher, D. Lavery, D. Millar, A. Alvarado, K. Parsons, R. Killey, and P. Bayvel, “Reach enhancement of 100% for a DP-64 QAM super-channel using MC-DBP,” in Optical Fiber Communication Conference (Optical Society of America, 2015), paper Th4D.5.

Kimble, H. J.

S. L. Braunstein and H. J. Kimble, “Dense coding for continuous variables,” Phys. Rev. A 61, 042302 (2000).
[Crossref]

Kippenberg, T. J.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546, 274–279 (2017).
[Crossref]

Knittel, J.

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7, 229–233 (2013).
[Crossref]

Koike-Akino, T.

D. Millar, R. Maher, D. Lavery, T. Koike-Akino, A. Alvarado, M. Paskov, K. Kojima, K. Parsons, B. C. Thomsen, S. J. Savory, and P. Bayvel, “Transceiver-limited high spectral efficiency Nyquist-WDM systems,” in Optical Fiber Communication Conference (Optical Society of America, 2015), paper Th2A.13.

Koizumi, Y.

Kojima, K.

D. Millar, R. Maher, D. Lavery, T. Koike-Akino, A. Alvarado, M. Paskov, K. Kojima, K. Parsons, B. C. Thomsen, S. J. Savory, and P. Bayvel, “Transceiver-limited high spectral efficiency Nyquist-WDM systems,” in Optical Fiber Communication Conference (Optical Society of America, 2015), paper Th2A.13.

Konwinski, A.

M. Armbrust, A. Fox, R. Griffith, A. D. Joseph, R. Katz, A. Konwinski, G. Lee, D. Patterson, A. Rabkin, I. Stoica, and M. Zaharia, “A view of cloud computing,” Commun. ACM 53, 50–58 (2010).
[Crossref]

Koos, C.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546, 274–279 (2017).
[Crossref]

Kordts, A.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546, 274–279 (2017).
[Crossref]

Kosloski, J.

F. Becerra, J. Fan, G. Baumgartner, J. Goldhar, J. Kosloski, and A. Migdall, “Experimental demonstration of a receiver beating the standard quantum limit for multiple nonorthogonal state discrimination,” Nat. Photonics 7, 147–152 (2013).
[Crossref]

Kosloski, J. T.

F. E. Becerra, J. Fan, G. Baumgartner, S. V. Polyakov, J. Goldhar, J. T. Kosloski, and A. Migdall, “M-ary-state phase-shift-keying discrimination below the homodyne limit,” Phys. Rev. A 84, 062324 (2011).
[Crossref]

Kouwenhoven, L.

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
[Crossref]

Kristensen, P.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref]

Kröll, S.

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
[Crossref]

Krummrich, P. M.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).
[Crossref]

Kschischang, F. R.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).
[Crossref]

Lavery, D.

R. Maher, A. Alvarado, D. Lavery, and P. Bayvel, “Increasing the information rates of optical communications via coded modulation: a study of transceiver performance,” Sci. Rep. 6, 21278 (2016).
[Crossref]

R. Maher, D. Lavery, D. Millar, A. Alvarado, K. Parsons, R. Killey, and P. Bayvel, “Reach enhancement of 100% for a DP-64 QAM super-channel using MC-DBP,” in Optical Fiber Communication Conference (Optical Society of America, 2015), paper Th4D.5.

D. Millar, R. Maher, D. Lavery, T. Koike-Akino, A. Alvarado, M. Paskov, K. Kojima, K. Parsons, B. C. Thomsen, S. J. Savory, and P. Bayvel, “Transceiver-limited high spectral efficiency Nyquist-WDM systems,” in Optical Fiber Communication Conference (Optical Society of America, 2015), paper Th2A.13.

Lee, G.

M. Armbrust, A. Fox, R. Griffith, A. D. Joseph, R. Katz, A. Konwinski, G. Lee, D. Patterson, A. Rabkin, I. Stoica, and M. Zaharia, “A view of cloud computing,” Commun. ACM 53, 50–58 (2010).
[Crossref]

Leuchs, G.

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
[Crossref]

Lewenstein, M.

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
[Crossref]

Li, K.

Y. Zuo, K. Li, and B. Zhu, “16-QAM quantum receiver with hybrid structure outperforming the standard quantum limit,” MATEC Web Conf. 61, 06008 (2016).
[Crossref]

Lord, A.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).
[Crossref]

Loss, D.

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
[Crossref]

Lütkenhaus, N.

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
[Crossref]

Maher, R.

R. Maher, A. Alvarado, D. Lavery, and P. Bayvel, “Increasing the information rates of optical communications via coded modulation: a study of transceiver performance,” Sci. Rep. 6, 21278 (2016).
[Crossref]

D. Millar, R. Maher, D. Lavery, T. Koike-Akino, A. Alvarado, M. Paskov, K. Kojima, K. Parsons, B. C. Thomsen, S. J. Savory, and P. Bayvel, “Transceiver-limited high spectral efficiency Nyquist-WDM systems,” in Optical Fiber Communication Conference (Optical Society of America, 2015), paper Th2A.13.

R. Maher, D. Lavery, D. Millar, A. Alvarado, K. Parsons, R. Killey, and P. Bayvel, “Reach enhancement of 100% for a DP-64 QAM super-channel using MC-DBP,” in Optical Fiber Communication Conference (Optical Society of America, 2015), paper Th4D.5.

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

Marin-Palomo, P.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546, 274–279 (2017).
[Crossref]

Marquardt, C.

C. R. Müller and C. Marquardt, “A robust quantum receiver for phase shift keyed signals,” New J. Phys. 17, 032003 (2015).
[Crossref]

Massar, S.

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
[Crossref]

Mecozzi, A.

Migdall, A.

F. Becerra, J. Fan, and A. Migdall, “Photon number resolution enables quantum receiver for realistic coherent optical communications,” Nat. Photonics 9, 48–53 (2015).
[Crossref]

F. Becerra, J. Fan, G. Baumgartner, J. Goldhar, J. Kosloski, and A. Migdall, “Experimental demonstration of a receiver beating the standard quantum limit for multiple nonorthogonal state discrimination,” Nat. Photonics 7, 147–152 (2013).
[Crossref]

F. E. Becerra, J. Fan, G. Baumgartner, S. V. Polyakov, J. Goldhar, J. T. Kosloski, and A. Migdall, “M-ary-state phase-shift-keying discrimination below the homodyne limit,” Phys. Rev. A 84, 062324 (2011).
[Crossref]

Millar, D.

R. Maher, D. Lavery, D. Millar, A. Alvarado, K. Parsons, R. Killey, and P. Bayvel, “Reach enhancement of 100% for a DP-64 QAM super-channel using MC-DBP,” in Optical Fiber Communication Conference (Optical Society of America, 2015), paper Th4D.5.

D. Millar, R. Maher, D. Lavery, T. Koike-Akino, A. Alvarado, M. Paskov, K. Kojima, K. Parsons, B. C. Thomsen, S. J. Savory, and P. Bayvel, “Transceiver-limited high spectral efficiency Nyquist-WDM systems,” in Optical Fiber Communication Conference (Optical Society of America, 2015), paper Th2A.13.

Miyazaki, T.

Mooij, J. E.

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
[Crossref]

Mori, S.

Müller, C. R.

C. R. Müller and C. Marquardt, “A robust quantum receiver for phase shift keyed signals,” New J. Phys. 17, 032003 (2015).
[Crossref]

Nakazawa, M.

Osaki, M.

K. Kato, M. Osaki, M. Sasaki, and O. Hirota, “Quantum detection and mutual information for QAM and PSK signals,” IEEE Trans. Commun. 47, 248–254 (1999).
[Crossref]

Parsons, K.

D. Millar, R. Maher, D. Lavery, T. Koike-Akino, A. Alvarado, M. Paskov, K. Kojima, K. Parsons, B. C. Thomsen, S. J. Savory, and P. Bayvel, “Transceiver-limited high spectral efficiency Nyquist-WDM systems,” in Optical Fiber Communication Conference (Optical Society of America, 2015), paper Th2A.13.

R. Maher, D. Lavery, D. Millar, A. Alvarado, K. Parsons, R. Killey, and P. Bayvel, “Reach enhancement of 100% for a DP-64 QAM super-channel using MC-DBP,” in Optical Fiber Communication Conference (Optical Society of America, 2015), paper Th4D.5.

Paskov, M.

D. Millar, R. Maher, D. Lavery, T. Koike-Akino, A. Alvarado, M. Paskov, K. Kojima, K. Parsons, B. C. Thomsen, S. J. Savory, and P. Bayvel, “Transceiver-limited high spectral efficiency Nyquist-WDM systems,” in Optical Fiber Communication Conference (Optical Society of America, 2015), paper Th2A.13.

Patterson, D.

M. Armbrust, A. Fox, R. Griffith, A. D. Joseph, R. Katz, A. Konwinski, G. Lee, D. Patterson, A. Rabkin, I. Stoica, and M. Zaharia, “A view of cloud computing,” Commun. ACM 53, 50–58 (2010).
[Crossref]

Pfeiffer, M. H. P.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546, 274–279 (2017).
[Crossref]

Pfeifle, J.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546, 274–279 (2017).
[Crossref]

Plenio, M. B.

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
[Crossref]

Polyakov, S. V.

F. E. Becerra, J. Fan, G. Baumgartner, S. V. Polyakov, J. Goldhar, J. T. Kosloski, and A. Migdall, “M-ary-state phase-shift-keying discrimination below the homodyne limit,” Phys. Rev. A 84, 062324 (2011).
[Crossref]

Polzik, E.

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
[Crossref]

Popescu, S.

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
[Crossref]

Prat, J.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).
[Crossref]

Proakis, J.

J. Proakis, Digital Communications, Electrical Engineering Series (McGraw-Hill, 2001).

Quine, Z.

A. Goun, D. I. Bondar, A. O. Er, Z. Quine, and H. A. Rabitz, “Photonic reagents for concentration measurement of fluorescent proteins with overlapping spectra,” Sci. Rep. 6, 25827 (2016).
[Crossref]

Rabitz, H. A.

A. Goun, D. I. Bondar, A. O. Er, Z. Quine, and H. A. Rabitz, “Photonic reagents for concentration measurement of fluorescent proteins with overlapping spectra,” Sci. Rep. 6, 25827 (2016).
[Crossref]

Rabkin, A.

M. Armbrust, A. Fox, R. Griffith, A. D. Joseph, R. Katz, A. Konwinski, G. Lee, D. Patterson, A. Rabkin, I. Stoica, and M. Zaharia, “A view of cloud computing,” Commun. ACM 53, 50–58 (2010).
[Crossref]

Ramachandran, S.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref]

Rempe, G.

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
[Crossref]

Ren, Y.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref]

Reynaud, S.

M. T. Jaekel and S. Reynaud, “Quantum limits in interferometric measurements,” Europhys. Lett. 13, 301–306 (1990).
[Crossref]

Richardson, D. J.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).
[Crossref]

Roberts, K.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).
[Crossref]

Robertson, H. P.

H. P. Robertson, “The uncertainty principle,” Phys. Rev. 34, 163–164 (1929).
[Crossref]

Rosenberger, R.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546, 274–279 (2017).
[Crossref]

Ross, S.

S. Ross, Introduction to Probability Models (Academic, 2007).

Rush, J.

R. J. Cesarone, D. S. Abraham, S. Shambayati, and J. Rush, “Deep-space optical communications,” in International Conference on Space Optical Systems and Applications (ICSOS) (2011), pp. 410–423.

Sakamoto, T.

Sasaki, M.

K. Tsujino, D. Fukuda, G. Fujii, S. Inoue, M. Fujiwara, M. Takeoka, and M. Sasaki, “Quantum receiver beyond the standard quantum limit of coherent optical communication,” Phys. Rev. Lett. 106, 250503 (2011).
[Crossref]

K. Tsujino, D. Fukuda, G. Fujii, S. Inoue, M. Fujiwara, M. Takeoka, and M. Sasaki, “Sub-shot-noise-limit discrimination of on-off keyed coherent signals via a quantum receiver with a superconducting transition edge sensor,” Opt. Express 18, 8107–8114 (2010).
[Crossref]

K. Kato, M. Osaki, M. Sasaki, and O. Hirota, “Quantum detection and mutual information for QAM and PSK signals,” IEEE Trans. Commun. 47, 248–254 (1999).
[Crossref]

Savory, S. J.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).
[Crossref]

D. Millar, R. Maher, D. Lavery, T. Koike-Akino, A. Alvarado, M. Paskov, K. Kojima, K. Parsons, B. C. Thomsen, S. J. Savory, and P. Bayvel, “Transceiver-limited high spectral efficiency Nyquist-WDM systems,” in Optical Fiber Communication Conference (Optical Society of America, 2015), paper Th2A.13.

Schumacher, B.

P. Hausladen, R. Jozsa, B. Schumacher, M. Westmoreland, and W. K. Wootters, “Classical information capacity of a quantum channel,” Phys. Rev. A 54, 1869–1876 (1996).
[Crossref]

Secondini, M.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).
[Crossref]

Sergienko, A.

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
[Crossref]

Shambayati, S.

R. J. Cesarone, D. S. Abraham, S. Shambayati, and J. Rush, “Deep-space optical communications,” in International Conference on Space Optical Systems and Applications (ICSOS) (2011), pp. 410–423.

Shtaif, M.

Srinivasan, S.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).
[Crossref]

Stoica, I.

M. Armbrust, A. Fox, R. Griffith, A. D. Joseph, R. Katz, A. Konwinski, G. Lee, D. Patterson, A. Rabkin, I. Stoica, and M. Zaharia, “A view of cloud computing,” Commun. ACM 53, 50–58 (2010).
[Crossref]

Suter, D.

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
[Crossref]

Takeoka, M.

S. Guha, J. L. Habif, and M. Takeoka, “Approaching Helstrom limits to optical pulse-position demodulation using single photon detection and optical feedback,” J. Mod. Opt. 58, 257–265 (2011).
[Crossref]

K. Tsujino, D. Fukuda, G. Fujii, S. Inoue, M. Fujiwara, M. Takeoka, and M. Sasaki, “Quantum receiver beyond the standard quantum limit of coherent optical communication,” Phys. Rev. Lett. 106, 250503 (2011).
[Crossref]

K. Tsujino, D. Fukuda, G. Fujii, S. Inoue, M. Fujiwara, M. Takeoka, and M. Sasaki, “Sub-shot-noise-limit discrimination of on-off keyed coherent signals via a quantum receiver with a superconducting transition edge sensor,” Opt. Express 18, 8107–8114 (2010).
[Crossref]

Taylor, M. A.

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7, 229–233 (2013).
[Crossref]

Thomsen, B. C.

D. Millar, R. Maher, D. Lavery, T. Koike-Akino, A. Alvarado, M. Paskov, K. Kojima, K. Parsons, B. C. Thomsen, S. J. Savory, and P. Bayvel, “Transceiver-limited high spectral efficiency Nyquist-WDM systems,” in Optical Fiber Communication Conference (Optical Society of America, 2015), paper Th2A.13.

Tomkos, I.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).
[Crossref]

Toyoda, K.

Trocha, P.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546, 274–279 (2017).
[Crossref]

Tsujino, K.

K. Tsujino, D. Fukuda, G. Fujii, S. Inoue, M. Fujiwara, M. Takeoka, and M. Sasaki, “Quantum receiver beyond the standard quantum limit of coherent optical communication,” Phys. Rev. Lett. 106, 250503 (2011).
[Crossref]

K. Tsujino, D. Fukuda, G. Fujii, S. Inoue, M. Fujiwara, M. Takeoka, and M. Sasaki, “Sub-shot-noise-limit discrimination of on-off keyed coherent signals via a quantum receiver with a superconducting transition edge sensor,” Opt. Express 18, 8107–8114 (2010).
[Crossref]

Tsukamoto, S.

Tur, M.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref]

Twamley, J.

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
[Crossref]

Vijayan, K.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546, 274–279 (2017).
[Crossref]

Wendin, G.

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
[Crossref]

Werner, R.

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
[Crossref]

Westmoreland, M.

P. Hausladen, R. Jozsa, B. Schumacher, M. Westmoreland, and W. K. Wootters, “Classical information capacity of a quantum channel,” Phys. Rev. A 54, 1869–1876 (1996).
[Crossref]

Willner, A. E.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref]

Winter, A.

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
[Crossref]

Winzer, P.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).
[Crossref]

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

Wolf, S.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546, 274–279 (2017).
[Crossref]

Wootters, W. K.

P. Hausladen, R. Jozsa, B. Schumacher, M. Westmoreland, and W. K. Wootters, “Classical information capacity of a quantum channel,” Phys. Rev. A 54, 1869–1876 (1996).
[Crossref]

Wrachtrup, J.

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
[Crossref]

Yoshida, M.

Yue, Y.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref]

Zaharia, M.

M. Armbrust, A. Fox, R. Griffith, A. D. Joseph, R. Katz, A. Konwinski, G. Lee, D. Patterson, A. Rabkin, I. Stoica, and M. Zaharia, “A view of cloud computing,” Commun. ACM 53, 50–58 (2010).
[Crossref]

Zeilinger, A.

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
[Crossref]

Zhu, B.

Y. Zuo, K. Li, and B. Zhu, “16-QAM quantum receiver with hybrid structure outperforming the standard quantum limit,” MATEC Web Conf. 61, 06008 (2016).
[Crossref]

Zoller, P.

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
[Crossref]

Zuo, Y.

Y. Zuo, K. Li, and B. Zhu, “16-QAM quantum receiver with hybrid structure outperforming the standard quantum limit,” MATEC Web Conf. 61, 06008 (2016).
[Crossref]

Commun. ACM (1)

M. Armbrust, A. Fox, R. Griffith, A. D. Joseph, R. Katz, A. Konwinski, G. Lee, D. Patterson, A. Rabkin, I. Stoica, and M. Zaharia, “A view of cloud computing,” Commun. ACM 53, 50–58 (2010).
[Crossref]

Eur. Phys. J. D (1)

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Kouwenhoven, S. Kröll, G. Leuchs, M. Lewenstein, D. Loss, N. Lütkenhaus, S. Massar, J. E. Mooij, M. B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zeilinger, “Quantum information processing and communication,” Eur. Phys. J. D 36, 203–228 (2005).
[Crossref]

Europhys. Lett. (1)

M. T. Jaekel and S. Reynaud, “Quantum limits in interferometric measurements,” Europhys. Lett. 13, 301–306 (1990).
[Crossref]

IEEE Commun. Surv. Tutorials (1)

H. Kaushal and G. Kaddoum, “Optical communication in space: challenges and mitigation techniques,” IEEE Commun. Surv. Tutorials 19, 57–96 (2017).
[Crossref]

IEEE Photon. J. (1)

Q. Chen, J. He, R. Deng, M. Chen, and L. Chen, “FFT-size efficient 4096-QAM OFDM for low-cost DML-based IMDD system,” IEEE Photon. J. 8, 7804010 (2016).
[Crossref]

IEEE Spectrum (1)

S. Cherry, “Edholm’s law of bandwidth,” IEEE Spectrum 41, 58–60 (2004).
[Crossref]

IEEE Trans. Commun. (1)

K. Kato, M. Osaki, M. Sasaki, and O. Hirota, “Quantum detection and mutual information for QAM and PSK signals,” IEEE Trans. Commun. 47, 248–254 (1999).
[Crossref]

J. Lightwave Technol. (1)

J. Mod. Opt. (1)

S. Guha, J. L. Habif, and M. Takeoka, “Approaching Helstrom limits to optical pulse-position demodulation using single photon detection and optical feedback,” J. Mod. Opt. 58, 257–265 (2011).
[Crossref]

J. Opt. (1)

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18, 063002 (2016).
[Crossref]

J. Stat. Phys. (1)

C. W. Helstrom, “Quantum detection and estimation theory,” J. Stat. Phys. 1, 231–252 (1969).
[Crossref]

MATEC Web Conf. (1)

Y. Zuo, K. Li, and B. Zhu, “16-QAM quantum receiver with hybrid structure outperforming the standard quantum limit,” MATEC Web Conf. 61, 06008 (2016).
[Crossref]

Nat. Photonics (3)

F. Becerra, J. Fan, G. Baumgartner, J. Goldhar, J. Kosloski, and A. Migdall, “Experimental demonstration of a receiver beating the standard quantum limit for multiple nonorthogonal state discrimination,” Nat. Photonics 7, 147–152 (2013).
[Crossref]

F. Becerra, J. Fan, and A. Migdall, “Photon number resolution enables quantum receiver for realistic coherent optical communications,” Nat. Photonics 9, 48–53 (2015).
[Crossref]

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7, 229–233 (2013).
[Crossref]

Nature (1)

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546, 274–279 (2017).
[Crossref]

New J. Phys. (1)

C. R. Müller and C. Marquardt, “A robust quantum receiver for phase shift keyed signals,” New J. Phys. 17, 032003 (2015).
[Crossref]

Opt. Express (3)

Optica (1)

Phys. Rev. (1)

H. P. Robertson, “The uncertainty principle,” Phys. Rev. 34, 163–164 (1929).
[Crossref]

Phys. Rev. A (3)

S. L. Braunstein and H. J. Kimble, “Dense coding for continuous variables,” Phys. Rev. A 61, 042302 (2000).
[Crossref]

F. E. Becerra, J. Fan, G. Baumgartner, S. V. Polyakov, J. Goldhar, J. T. Kosloski, and A. Migdall, “M-ary-state phase-shift-keying discrimination below the homodyne limit,” Phys. Rev. A 84, 062324 (2011).
[Crossref]

P. Hausladen, R. Jozsa, B. Schumacher, M. Westmoreland, and W. K. Wootters, “Classical information capacity of a quantum channel,” Phys. Rev. A 54, 1869–1876 (1996).
[Crossref]

Phys. Rev. D (1)

C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23, 1693–1708 (1981).
[Crossref]

Phys. Rev. Lett. (2)

K. Tsujino, D. Fukuda, G. Fujii, S. Inoue, M. Fujiwara, M. Takeoka, and M. Sasaki, “Quantum receiver beyond the standard quantum limit of coherent optical communication,” Phys. Rev. Lett. 106, 250503 (2011).
[Crossref]

C. M. Caves, “Quantum-mechanical radiation-pressure fluctuations in an interferometer,” Phys. Rev. Lett. 45, 75–79 (1980).
[Crossref]

Probl. Peredachi Inform. (1)

A. S. Holevo, “On capacity of a quantum communications channel,” Probl. Peredachi Inform. 15, 3–11 (1979).

Radiotekhnika i Elektronika (1)

V. P. Belavkin, “Optimum distinction of non-orthogonal quantum signals,” Radiotekhnika i Elektronika 20, 1177–1185 (1975).

Sci. Rep. (2)

R. Maher, A. Alvarado, D. Lavery, and P. Bayvel, “Increasing the information rates of optical communications via coded modulation: a study of transceiver performance,” Sci. Rep. 6, 21278 (2016).
[Crossref]

A. Goun, D. I. Bondar, A. O. Er, Z. Quine, and H. A. Rabitz, “Photonic reagents for concentration measurement of fluorescent proteins with overlapping spectra,” Sci. Rep. 6, 25827 (2016).
[Crossref]

Science (1)

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref]

Other (9)

D. Millar, R. Maher, D. Lavery, T. Koike-Akino, A. Alvarado, M. Paskov, K. Kojima, K. Parsons, B. C. Thomsen, S. J. Savory, and P. Bayvel, “Transceiver-limited high spectral efficiency Nyquist-WDM systems,” in Optical Fiber Communication Conference (Optical Society of America, 2015), paper Th2A.13.

R. Maher, D. Lavery, D. Millar, A. Alvarado, K. Parsons, R. Killey, and P. Bayvel, “Reach enhancement of 100% for a DP-64 QAM super-channel using MC-DBP,” in Optical Fiber Communication Conference (Optical Society of America, 2015), paper Th4D.5.

Homer, “The Iliad,” (Book XVIII, Lines 200–213, VIII–VII B.C.), http://www.perseus.tufts.edu/hopper/text?doc=urn:cts:greekLit:tlg0012.tlg001.perseus-eng1:18.181-18.218 .

R. J. Cesarone, D. S. Abraham, S. Shambayati, and J. Rush, “Deep-space optical communications,” in International Conference on Space Optical Systems and Applications (ICSOS) (2011), pp. 410–423.

J. Proakis, Digital Communications, Electrical Engineering Series (McGraw-Hill, 2001).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

S. J. Dolinar, “Quantum limits in interferometric measurements,” Technical Report (Research Laboratory of Electronics, MIT, 1973).

R. S. Kennedy, “Quantum limits in interferometric measurements,” Technical Report (Research Laboratory of Electronics, MIT, 1972).

S. Ross, Introduction to Probability Models (Academic, 2007).

Supplementary Material (1)

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Figures (7)

Fig. 1.
Fig. 1. (a) Constellation diagram introducing the M-ary CFSK. Symbols are encoded as coherent states of different frequencies ωi and phases θi, resulting in rotation with time around the origin with rates that correspond to their detuning from the carrier frequency (shown in red). (b) Quantum receiver’s principle of operation. A displacement corresponding to the most probable state of the input field |α(ωs,θs) is followed with a single-photon detector. A kth click on the detector invalidates the hypothesis hk. The probability of a click varies with time. Hence, the time of detection tk contains important information about the input state (inset). To find the best a posteriori hypothesis, we implement a Bayesian adaptive strategy for a continuous, time-resolved measurement; see text.
Fig. 2.
Fig. 2. Energy dependence of symbol error rates along with fundamental bounds for different encoding techniques with the 4-bit (M=16) alphabet. CFSK receiver: purple squares; CFSK receiver with practical visibility: red diamonds; PSK receiver: blue dots. Discrimination error bounds are shown with lines: PSK (blue) and CFSK (purple). SQL, dashed lines; HB, solid lines.
Fig. 3.
Fig. 3. Energy efficiency scaling. A ratio of HBs of CFSK and PSK over a range of input energies and alphabet lengths. A significant advantage of M-ary CFSK over M-ary PSK in terms of error probability is evident for all input signal energies for all M>4 alphabets, log2M>2. The region of CFSK advantage is all the area to the right of the black dashed line, which indicates a HBs’ ratio of 1. White lines correspond to constant input energy per bit to aid in comparison (see text).
Fig. 4.
Fig. 4. Log SER map versus the optimization parameters for a CFSK receiver with a 4-bit (M=16) alphabet with the input energy of 2 photons per bit. The optimal parameter range for energy sensitivity: white dashed contour. The secondary optimal parameter range for energy sensitivity with a modest increase of symbol error rate but with twice smaller frequency separation between the states ΔωT: green dashed contour. The optimization parameter space contains the set that corresponds to PSK (blue circle). Our receiver beats the PSK receiver in SER by over three orders of magnitude. Parameter sets for the classical orthogonal FSK and OFDM (dashed orange line) and the minimum shift keying (light blue triangle) are marked to aid with comparison.
Fig. 5.
Fig. 5. Schematic comparison of spectral separation of classical versus quantum frequency-shift-based receivers.
Fig. 6.
Fig. 6. Symbol error rate performance of quantum PSK (blue dots) and CFSK (purple squares) receivers for different encoding capacities log2M with a constant input energy per bit, cf. white lines in Fig. 3. In addition, SQLs (dashed lines) and HBs (solid lines) are shown. The symbol error rate of a quantum PSK receiver significantly worsens with the longer alphabets while that of our CFSK receiver provides scaling with the alphabet size. Thin lines that connect dots and squares are guides for the viewer’s eye.
Fig. 7.
Fig. 7. Experimental implementation of an M-ary CFSK receiver. The receiver discriminates between CFSK states prepared by a frequency-phase modulator implemented with a double-pass acousto-optical modulator (AOM). An identical AOM arrangement implements the adaptive LO. The displacement is performed by interfering the input state with the LO on a 99:1 beamsplitter (BS) followed by a single-photon detector (SPD). PBS, polarization beam splitter; PS, phase shifter; λ/2 and λ/4, half- and quarter-wave-plates; BD, beam dump.

Equations (1)

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ζtk(m)=(n(m,h,tk)/T)etk1tkn(m,h,τ)dτ/Tζtk1(m)j=1M(n(j,h,tk)/T)etk1tkn(j,h,τ)dτ/Tζtk1(j),

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