Abstract

We analyze homodyne detection of macroscopically bright multimode nonclassical states of light and propose their application in quantum communication. We observe that the homodyne detection is sensitive to a mode-matching of the bright light to the highly intense local oscillator. Unmatched bright modes of light result in additional noise which technically limits detection of Gaussian entanglement at macroscopic level. When the mode-matching is sufficient, we show that multimode quantum key distribution with bright beams is feasible. It finally merges the quantum communication with classical optical technology of visible beams of light.

© 2015 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
From quantum cloning to quantum key distribution with continuous variables: a review (Invited)

Nicolas J. Cerf and Philippe Grangier
J. Opt. Soc. Am. B 24(2) 324-334 (2007)

Quantum frequency down-conversion of bright amplitude-squeezed states

Dehuan Kong, Zongyang Li, Shaofeng Wang, Xuyang Wang, and Yongmin Li
Opt. Express 22(20) 24192-24201 (2014)

Engineering continuous and discrete variable quantum vortex states by nonlocal photon subtraction in a reconfigurable photonic chip

David Barral, Jesús Liñares, and Daniel Balado
J. Opt. Soc. Am. B 33(11) 2225-2235 (2016)

References

  • View by:
  • |
  • |
  • |

  1. N. J. Cerf, G. Leuchs, and E. S. Polzik, Quantum Information with Continuous Variables of Atoms and Light (Imperial College Press, 2007).
  2. J. Hald, J. Sørensen, C. Schori, and E. Polzik, “Spin squeezed atoms: a macroscopic entangled ensemble created by light,” Phys. Rev. Lett. 83, 1319 (1999).
    [Crossref]
  3. T. Fernholz, H. Krauter, K. Jensen, J. F. Sherson, A. S. Sørensen, and E. S. Polzik, “Spin squeezing of atomic ensembles via nuclear-electronic spin entanglement,” Phys. Rev. Lett. 101, 073601 (2008).
    [Crossref] [PubMed]
  4. T. Iskhakov, M. V. Chekhova, and G. Leuchs, “Generation and direct detection of broadband mesoscopic polarization-squeezed vacuum,” Phys. Rev. Lett. 102, 183602 (2009).
    [Crossref] [PubMed]
  5. G. Tóth and M. W. Mitchell, “Generation of macroscopic singlet states in atomic ensembles,” New J. Phys. 12, 053007 (2010).
    [Crossref]
  6. T. S. Iskhakov, I. N. Agafonov, M. V. Chekhova, and G. Leuchs, “Polarization-entangled light pulses of 10 5 photons,” Phys. Rev. Lett. 109, 150502 (2012).
    [Crossref]
  7. N. Behbood, F. M. Ciurana, G. Colangelo, M. Napolitano, G. Tóth, R. Sewell, and M. Mitchell, “Generation of macroscopic singlet states in a cold atomic ensemble,” Phys. Rev. Lett. 113, 093601 (2014).
    [Crossref] [PubMed]
  8. G. Vasilakis, H. Shen, K. Jensen, M. Balabas, D. Salart, B. Chen, and E. S. Polzik, “Generation of a squeezed state of an oscillator by stroboscopic back-action-evading measurement,” Nat. Phys. 11, 389–392 (2015).
    [Crossref]
  9. M. Vasilyev, S.-K. Choi, P. Kumar, and G. M. D’Ariano, “Tomographic measurement of joint photon statistics of the twin-beam quantum state,” Phys. Rev. Lett. 84, 2354 (2000).
    [Crossref] [PubMed]
  10. S. L. Braunstein and P. Van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513 (2005).
    [Crossref]
  11. L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3, 1083 (2012).
    [Crossref] [PubMed]
  12. F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using gaussian-modulated coherent states,” Nature 421, 238–241 (2003).
    [Crossref] [PubMed]
  13. V. C. Usenko, L. Ruppert, and R. Filip, “Entanglement-based continuous-variable quantum key distribution with multimode states and detectors,” Phys. Rev. A 90, 062326 (2014).
    [Crossref]
  14. M. Raymer, J. Cooper, H. Carmichael, M. Beck, and D. Smithey, “Ultrafast measurement of optical-field statistics by dc-balanced homodyne detection,” J. Opt. Soc. Am. B 12, 1801–1812 (1995).
    [Crossref]
  15. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145 (2002).
    [Crossref]
  16. B. Qi, P. Lougovski, R. Pooser, W. Grice, and M. Bobrek, “Generating the local oscillator” locally” in continuous-variable quantum key distribution based on coherent detection,” arXiv preprint arXiv:1503.00662 (2015).
  17. M. Collett, R. Loudon, and C. Gardiner, “Quantum theory of optical homodyne and heterodyne detection,” J. Mod. Opt. 34, 881–902 (1987).
    [Crossref]
  18. G. Vidal and R. F. Werner, “Computable measure of entanglement,” Phys. Rev. A 65, 032314 (2002).
    [Crossref]
  19. F. Grosshans, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and P. Grangier, “Virtual entanglement and reconciliation protocols for quantum cryptography with continuous variables,” Quantum Info. Comput. 3, 535–552 (2003).
  20. M. M. Wolf, G. Giedke, and J. I. Cirac, “Extremality of gaussian quantum states,” Phys. Rev. Lett. 96, 080502 (2006).
    [Crossref] [PubMed]
  21. M. Navascués, F. Grosshans, and A. Acin, “Optimality of gaussian attacks in continuous-variable quantum cryptography,” Phys. Rev. Lett. 97, 190502 (2006).
    [Crossref] [PubMed]
  22. R. Garcia-Patron and N. J. Cerf, “Unconditional optimality of gaussian attacks against continuous-variable quantum key distribution,” Phys. Rev. Lett. 97, 190503 (2006).
    [Crossref] [PubMed]
  23. X.-C. Ma, S.-H. Sun, M.-S. Jiang, and L.-M. Liang, “Wavelength attack on practical continuous-variable quantum-key-distribution system with a heterodyne protocol,” Phys. Rev. A 87, 052309 (2013).
    [Crossref]
  24. J.-Z. Huang, C. Weedbrook, Z.-Q. Yin, S. Wang, H.-W. Li, W. Chen, G.-C. Guo, and Z.-F. Han, “Quantum hacking of a continuous-variable quantum-key-distribution system using a wavelength attack,” Phys. Rev. A 87, 062329 (2013).
    [Crossref]
  25. J.-Z. Huang, S. Kunz-Jacques, P. Jouguet, C. Weedbrook, Z.-Q. Yin, S. Wang, W. Chen, G.-C. Guo, and Z.-F. Han, “Quantum hacking on quantum key distribution using homodyne detection,” Phys. Rev. A 89, 032304 (2014).
    [Crossref]
  26. P. Jouguet, S. Kunz-Jacques, and A. Leverrier, “Long-distance continuous-variable quantum key distribution with a gaussian modulation,” Phys. Rev. A 84, 062317 (2011).
    [Crossref]
  27. J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and et al., “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76, 042305 (2007).
    [Crossref]

2015 (1)

G. Vasilakis, H. Shen, K. Jensen, M. Balabas, D. Salart, B. Chen, and E. S. Polzik, “Generation of a squeezed state of an oscillator by stroboscopic back-action-evading measurement,” Nat. Phys. 11, 389–392 (2015).
[Crossref]

2014 (3)

N. Behbood, F. M. Ciurana, G. Colangelo, M. Napolitano, G. Tóth, R. Sewell, and M. Mitchell, “Generation of macroscopic singlet states in a cold atomic ensemble,” Phys. Rev. Lett. 113, 093601 (2014).
[Crossref] [PubMed]

V. C. Usenko, L. Ruppert, and R. Filip, “Entanglement-based continuous-variable quantum key distribution with multimode states and detectors,” Phys. Rev. A 90, 062326 (2014).
[Crossref]

J.-Z. Huang, S. Kunz-Jacques, P. Jouguet, C. Weedbrook, Z.-Q. Yin, S. Wang, W. Chen, G.-C. Guo, and Z.-F. Han, “Quantum hacking on quantum key distribution using homodyne detection,” Phys. Rev. A 89, 032304 (2014).
[Crossref]

2013 (2)

X.-C. Ma, S.-H. Sun, M.-S. Jiang, and L.-M. Liang, “Wavelength attack on practical continuous-variable quantum-key-distribution system with a heterodyne protocol,” Phys. Rev. A 87, 052309 (2013).
[Crossref]

J.-Z. Huang, C. Weedbrook, Z.-Q. Yin, S. Wang, H.-W. Li, W. Chen, G.-C. Guo, and Z.-F. Han, “Quantum hacking of a continuous-variable quantum-key-distribution system using a wavelength attack,” Phys. Rev. A 87, 062329 (2013).
[Crossref]

2012 (2)

L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3, 1083 (2012).
[Crossref] [PubMed]

T. S. Iskhakov, I. N. Agafonov, M. V. Chekhova, and G. Leuchs, “Polarization-entangled light pulses of 10 5 photons,” Phys. Rev. Lett. 109, 150502 (2012).
[Crossref]

2011 (1)

P. Jouguet, S. Kunz-Jacques, and A. Leverrier, “Long-distance continuous-variable quantum key distribution with a gaussian modulation,” Phys. Rev. A 84, 062317 (2011).
[Crossref]

2010 (1)

G. Tóth and M. W. Mitchell, “Generation of macroscopic singlet states in atomic ensembles,” New J. Phys. 12, 053007 (2010).
[Crossref]

2009 (1)

T. Iskhakov, M. V. Chekhova, and G. Leuchs, “Generation and direct detection of broadband mesoscopic polarization-squeezed vacuum,” Phys. Rev. Lett. 102, 183602 (2009).
[Crossref] [PubMed]

2008 (1)

T. Fernholz, H. Krauter, K. Jensen, J. F. Sherson, A. S. Sørensen, and E. S. Polzik, “Spin squeezing of atomic ensembles via nuclear-electronic spin entanglement,” Phys. Rev. Lett. 101, 073601 (2008).
[Crossref] [PubMed]

2007 (1)

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and et al., “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76, 042305 (2007).
[Crossref]

2006 (3)

M. M. Wolf, G. Giedke, and J. I. Cirac, “Extremality of gaussian quantum states,” Phys. Rev. Lett. 96, 080502 (2006).
[Crossref] [PubMed]

M. Navascués, F. Grosshans, and A. Acin, “Optimality of gaussian attacks in continuous-variable quantum cryptography,” Phys. Rev. Lett. 97, 190502 (2006).
[Crossref] [PubMed]

R. Garcia-Patron and N. J. Cerf, “Unconditional optimality of gaussian attacks against continuous-variable quantum key distribution,” Phys. Rev. Lett. 97, 190503 (2006).
[Crossref] [PubMed]

2005 (1)

S. L. Braunstein and P. Van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513 (2005).
[Crossref]

2003 (2)

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using gaussian-modulated coherent states,” Nature 421, 238–241 (2003).
[Crossref] [PubMed]

F. Grosshans, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and P. Grangier, “Virtual entanglement and reconciliation protocols for quantum cryptography with continuous variables,” Quantum Info. Comput. 3, 535–552 (2003).

2002 (2)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145 (2002).
[Crossref]

G. Vidal and R. F. Werner, “Computable measure of entanglement,” Phys. Rev. A 65, 032314 (2002).
[Crossref]

2000 (1)

M. Vasilyev, S.-K. Choi, P. Kumar, and G. M. D’Ariano, “Tomographic measurement of joint photon statistics of the twin-beam quantum state,” Phys. Rev. Lett. 84, 2354 (2000).
[Crossref] [PubMed]

1999 (1)

J. Hald, J. Sørensen, C. Schori, and E. Polzik, “Spin squeezed atoms: a macroscopic entangled ensemble created by light,” Phys. Rev. Lett. 83, 1319 (1999).
[Crossref]

1995 (1)

1987 (1)

M. Collett, R. Loudon, and C. Gardiner, “Quantum theory of optical homodyne and heterodyne detection,” J. Mod. Opt. 34, 881–902 (1987).
[Crossref]

Acin, A.

M. Navascués, F. Grosshans, and A. Acin, “Optimality of gaussian attacks in continuous-variable quantum cryptography,” Phys. Rev. Lett. 97, 190502 (2006).
[Crossref] [PubMed]

Agafonov, I. N.

T. S. Iskhakov, I. N. Agafonov, M. V. Chekhova, and G. Leuchs, “Polarization-entangled light pulses of 10 5 photons,” Phys. Rev. Lett. 109, 150502 (2012).
[Crossref]

Andersen, U. L.

L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3, 1083 (2012).
[Crossref] [PubMed]

Balabas, M.

G. Vasilakis, H. Shen, K. Jensen, M. Balabas, D. Salart, B. Chen, and E. S. Polzik, “Generation of a squeezed state of an oscillator by stroboscopic back-action-evading measurement,” Nat. Phys. 11, 389–392 (2015).
[Crossref]

Beck, M.

Behbood, N.

N. Behbood, F. M. Ciurana, G. Colangelo, M. Napolitano, G. Tóth, R. Sewell, and M. Mitchell, “Generation of macroscopic singlet states in a cold atomic ensemble,” Phys. Rev. Lett. 113, 093601 (2014).
[Crossref] [PubMed]

Bloch, M.

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and et al., “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76, 042305 (2007).
[Crossref]

Bobrek, M.

B. Qi, P. Lougovski, R. Pooser, W. Grice, and M. Bobrek, “Generating the local oscillator” locally” in continuous-variable quantum key distribution based on coherent detection,” arXiv preprint arXiv:1503.00662 (2015).

Braunstein, S. L.

S. L. Braunstein and P. Van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513 (2005).
[Crossref]

Brouri, R.

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using gaussian-modulated coherent states,” Nature 421, 238–241 (2003).
[Crossref] [PubMed]

Carmichael, H.

Cerf, N. J.

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and et al., “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76, 042305 (2007).
[Crossref]

R. Garcia-Patron and N. J. Cerf, “Unconditional optimality of gaussian attacks against continuous-variable quantum key distribution,” Phys. Rev. Lett. 97, 190503 (2006).
[Crossref] [PubMed]

F. Grosshans, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and P. Grangier, “Virtual entanglement and reconciliation protocols for quantum cryptography with continuous variables,” Quantum Info. Comput. 3, 535–552 (2003).

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using gaussian-modulated coherent states,” Nature 421, 238–241 (2003).
[Crossref] [PubMed]

N. J. Cerf, G. Leuchs, and E. S. Polzik, Quantum Information with Continuous Variables of Atoms and Light (Imperial College Press, 2007).

Chekhova, M. V.

T. S. Iskhakov, I. N. Agafonov, M. V. Chekhova, and G. Leuchs, “Polarization-entangled light pulses of 10 5 photons,” Phys. Rev. Lett. 109, 150502 (2012).
[Crossref]

T. Iskhakov, M. V. Chekhova, and G. Leuchs, “Generation and direct detection of broadband mesoscopic polarization-squeezed vacuum,” Phys. Rev. Lett. 102, 183602 (2009).
[Crossref] [PubMed]

Chen, B.

G. Vasilakis, H. Shen, K. Jensen, M. Balabas, D. Salart, B. Chen, and E. S. Polzik, “Generation of a squeezed state of an oscillator by stroboscopic back-action-evading measurement,” Nat. Phys. 11, 389–392 (2015).
[Crossref]

Chen, W.

J.-Z. Huang, S. Kunz-Jacques, P. Jouguet, C. Weedbrook, Z.-Q. Yin, S. Wang, W. Chen, G.-C. Guo, and Z.-F. Han, “Quantum hacking on quantum key distribution using homodyne detection,” Phys. Rev. A 89, 032304 (2014).
[Crossref]

J.-Z. Huang, C. Weedbrook, Z.-Q. Yin, S. Wang, H.-W. Li, W. Chen, G.-C. Guo, and Z.-F. Han, “Quantum hacking of a continuous-variable quantum-key-distribution system using a wavelength attack,” Phys. Rev. A 87, 062329 (2013).
[Crossref]

Choi, S.-K.

M. Vasilyev, S.-K. Choi, P. Kumar, and G. M. D’Ariano, “Tomographic measurement of joint photon statistics of the twin-beam quantum state,” Phys. Rev. Lett. 84, 2354 (2000).
[Crossref] [PubMed]

Cirac, J. I.

M. M. Wolf, G. Giedke, and J. I. Cirac, “Extremality of gaussian quantum states,” Phys. Rev. Lett. 96, 080502 (2006).
[Crossref] [PubMed]

Ciurana, F. M.

N. Behbood, F. M. Ciurana, G. Colangelo, M. Napolitano, G. Tóth, R. Sewell, and M. Mitchell, “Generation of macroscopic singlet states in a cold atomic ensemble,” Phys. Rev. Lett. 113, 093601 (2014).
[Crossref] [PubMed]

Colangelo, G.

N. Behbood, F. M. Ciurana, G. Colangelo, M. Napolitano, G. Tóth, R. Sewell, and M. Mitchell, “Generation of macroscopic singlet states in a cold atomic ensemble,” Phys. Rev. Lett. 113, 093601 (2014).
[Crossref] [PubMed]

Collett, M.

M. Collett, R. Loudon, and C. Gardiner, “Quantum theory of optical homodyne and heterodyne detection,” J. Mod. Opt. 34, 881–902 (1987).
[Crossref]

Cooper, J.

D’Ariano, G. M.

M. Vasilyev, S.-K. Choi, P. Kumar, and G. M. D’Ariano, “Tomographic measurement of joint photon statistics of the twin-beam quantum state,” Phys. Rev. Lett. 84, 2354 (2000).
[Crossref] [PubMed]

Debuisschert, T.

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and et al., “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76, 042305 (2007).
[Crossref]

Diamanti, E.

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and et al., “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76, 042305 (2007).
[Crossref]

Fernholz, T.

T. Fernholz, H. Krauter, K. Jensen, J. F. Sherson, A. S. Sørensen, and E. S. Polzik, “Spin squeezing of atomic ensembles via nuclear-electronic spin entanglement,” Phys. Rev. Lett. 101, 073601 (2008).
[Crossref] [PubMed]

Filip, R.

V. C. Usenko, L. Ruppert, and R. Filip, “Entanglement-based continuous-variable quantum key distribution with multimode states and detectors,” Phys. Rev. A 90, 062326 (2014).
[Crossref]

L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3, 1083 (2012).
[Crossref] [PubMed]

Fossier, S.

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and et al., “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76, 042305 (2007).
[Crossref]

Garcia-Patron, R.

R. Garcia-Patron and N. J. Cerf, “Unconditional optimality of gaussian attacks against continuous-variable quantum key distribution,” Phys. Rev. Lett. 97, 190503 (2006).
[Crossref] [PubMed]

García-Patrón, R.

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and et al., “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76, 042305 (2007).
[Crossref]

Gardiner, C.

M. Collett, R. Loudon, and C. Gardiner, “Quantum theory of optical homodyne and heterodyne detection,” J. Mod. Opt. 34, 881–902 (1987).
[Crossref]

Giedke, G.

M. M. Wolf, G. Giedke, and J. I. Cirac, “Extremality of gaussian quantum states,” Phys. Rev. Lett. 96, 080502 (2006).
[Crossref] [PubMed]

Gisin, N.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145 (2002).
[Crossref]

Grangier, P.

F. Grosshans, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and P. Grangier, “Virtual entanglement and reconciliation protocols for quantum cryptography with continuous variables,” Quantum Info. Comput. 3, 535–552 (2003).

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using gaussian-modulated coherent states,” Nature 421, 238–241 (2003).
[Crossref] [PubMed]

Grice, W.

B. Qi, P. Lougovski, R. Pooser, W. Grice, and M. Bobrek, “Generating the local oscillator” locally” in continuous-variable quantum key distribution based on coherent detection,” arXiv preprint arXiv:1503.00662 (2015).

Grosshans, F.

M. Navascués, F. Grosshans, and A. Acin, “Optimality of gaussian attacks in continuous-variable quantum cryptography,” Phys. Rev. Lett. 97, 190502 (2006).
[Crossref] [PubMed]

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using gaussian-modulated coherent states,” Nature 421, 238–241 (2003).
[Crossref] [PubMed]

F. Grosshans, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and P. Grangier, “Virtual entanglement and reconciliation protocols for quantum cryptography with continuous variables,” Quantum Info. Comput. 3, 535–552 (2003).

Guo, G.-C.

J.-Z. Huang, S. Kunz-Jacques, P. Jouguet, C. Weedbrook, Z.-Q. Yin, S. Wang, W. Chen, G.-C. Guo, and Z.-F. Han, “Quantum hacking on quantum key distribution using homodyne detection,” Phys. Rev. A 89, 032304 (2014).
[Crossref]

J.-Z. Huang, C. Weedbrook, Z.-Q. Yin, S. Wang, H.-W. Li, W. Chen, G.-C. Guo, and Z.-F. Han, “Quantum hacking of a continuous-variable quantum-key-distribution system using a wavelength attack,” Phys. Rev. A 87, 062329 (2013).
[Crossref]

Hald, J.

J. Hald, J. Sørensen, C. Schori, and E. Polzik, “Spin squeezed atoms: a macroscopic entangled ensemble created by light,” Phys. Rev. Lett. 83, 1319 (1999).
[Crossref]

Han, Z.-F.

J.-Z. Huang, S. Kunz-Jacques, P. Jouguet, C. Weedbrook, Z.-Q. Yin, S. Wang, W. Chen, G.-C. Guo, and Z.-F. Han, “Quantum hacking on quantum key distribution using homodyne detection,” Phys. Rev. A 89, 032304 (2014).
[Crossref]

J.-Z. Huang, C. Weedbrook, Z.-Q. Yin, S. Wang, H.-W. Li, W. Chen, G.-C. Guo, and Z.-F. Han, “Quantum hacking of a continuous-variable quantum-key-distribution system using a wavelength attack,” Phys. Rev. A 87, 062329 (2013).
[Crossref]

Huang, J.-Z.

J.-Z. Huang, S. Kunz-Jacques, P. Jouguet, C. Weedbrook, Z.-Q. Yin, S. Wang, W. Chen, G.-C. Guo, and Z.-F. Han, “Quantum hacking on quantum key distribution using homodyne detection,” Phys. Rev. A 89, 032304 (2014).
[Crossref]

J.-Z. Huang, C. Weedbrook, Z.-Q. Yin, S. Wang, H.-W. Li, W. Chen, G.-C. Guo, and Z.-F. Han, “Quantum hacking of a continuous-variable quantum-key-distribution system using a wavelength attack,” Phys. Rev. A 87, 062329 (2013).
[Crossref]

Iskhakov, T.

T. Iskhakov, M. V. Chekhova, and G. Leuchs, “Generation and direct detection of broadband mesoscopic polarization-squeezed vacuum,” Phys. Rev. Lett. 102, 183602 (2009).
[Crossref] [PubMed]

Iskhakov, T. S.

T. S. Iskhakov, I. N. Agafonov, M. V. Chekhova, and G. Leuchs, “Polarization-entangled light pulses of 10 5 photons,” Phys. Rev. Lett. 109, 150502 (2012).
[Crossref]

Jensen, K.

G. Vasilakis, H. Shen, K. Jensen, M. Balabas, D. Salart, B. Chen, and E. S. Polzik, “Generation of a squeezed state of an oscillator by stroboscopic back-action-evading measurement,” Nat. Phys. 11, 389–392 (2015).
[Crossref]

T. Fernholz, H. Krauter, K. Jensen, J. F. Sherson, A. S. Sørensen, and E. S. Polzik, “Spin squeezing of atomic ensembles via nuclear-electronic spin entanglement,” Phys. Rev. Lett. 101, 073601 (2008).
[Crossref] [PubMed]

Jiang, M.-S.

X.-C. Ma, S.-H. Sun, M.-S. Jiang, and L.-M. Liang, “Wavelength attack on practical continuous-variable quantum-key-distribution system with a heterodyne protocol,” Phys. Rev. A 87, 052309 (2013).
[Crossref]

Jouguet, P.

J.-Z. Huang, S. Kunz-Jacques, P. Jouguet, C. Weedbrook, Z.-Q. Yin, S. Wang, W. Chen, G.-C. Guo, and Z.-F. Han, “Quantum hacking on quantum key distribution using homodyne detection,” Phys. Rev. A 89, 032304 (2014).
[Crossref]

P. Jouguet, S. Kunz-Jacques, and A. Leverrier, “Long-distance continuous-variable quantum key distribution with a gaussian modulation,” Phys. Rev. A 84, 062317 (2011).
[Crossref]

Karpov, E.

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and et al., “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76, 042305 (2007).
[Crossref]

Krauter, H.

T. Fernholz, H. Krauter, K. Jensen, J. F. Sherson, A. S. Sørensen, and E. S. Polzik, “Spin squeezing of atomic ensembles via nuclear-electronic spin entanglement,” Phys. Rev. Lett. 101, 073601 (2008).
[Crossref] [PubMed]

Kumar, P.

M. Vasilyev, S.-K. Choi, P. Kumar, and G. M. D’Ariano, “Tomographic measurement of joint photon statistics of the twin-beam quantum state,” Phys. Rev. Lett. 84, 2354 (2000).
[Crossref] [PubMed]

Kunz-Jacques, S.

J.-Z. Huang, S. Kunz-Jacques, P. Jouguet, C. Weedbrook, Z.-Q. Yin, S. Wang, W. Chen, G.-C. Guo, and Z.-F. Han, “Quantum hacking on quantum key distribution using homodyne detection,” Phys. Rev. A 89, 032304 (2014).
[Crossref]

P. Jouguet, S. Kunz-Jacques, and A. Leverrier, “Long-distance continuous-variable quantum key distribution with a gaussian modulation,” Phys. Rev. A 84, 062317 (2011).
[Crossref]

Lassen, M.

L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3, 1083 (2012).
[Crossref] [PubMed]

Leuchs, G.

T. S. Iskhakov, I. N. Agafonov, M. V. Chekhova, and G. Leuchs, “Polarization-entangled light pulses of 10 5 photons,” Phys. Rev. Lett. 109, 150502 (2012).
[Crossref]

T. Iskhakov, M. V. Chekhova, and G. Leuchs, “Generation and direct detection of broadband mesoscopic polarization-squeezed vacuum,” Phys. Rev. Lett. 102, 183602 (2009).
[Crossref] [PubMed]

N. J. Cerf, G. Leuchs, and E. S. Polzik, Quantum Information with Continuous Variables of Atoms and Light (Imperial College Press, 2007).

Leverrier, A.

P. Jouguet, S. Kunz-Jacques, and A. Leverrier, “Long-distance continuous-variable quantum key distribution with a gaussian modulation,” Phys. Rev. A 84, 062317 (2011).
[Crossref]

Li, H.-W.

J.-Z. Huang, C. Weedbrook, Z.-Q. Yin, S. Wang, H.-W. Li, W. Chen, G.-C. Guo, and Z.-F. Han, “Quantum hacking of a continuous-variable quantum-key-distribution system using a wavelength attack,” Phys. Rev. A 87, 062329 (2013).
[Crossref]

Liang, L.-M.

X.-C. Ma, S.-H. Sun, M.-S. Jiang, and L.-M. Liang, “Wavelength attack on practical continuous-variable quantum-key-distribution system with a heterodyne protocol,” Phys. Rev. A 87, 052309 (2013).
[Crossref]

Lodewyck, J.

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and et al., “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76, 042305 (2007).
[Crossref]

Loudon, R.

M. Collett, R. Loudon, and C. Gardiner, “Quantum theory of optical homodyne and heterodyne detection,” J. Mod. Opt. 34, 881–902 (1987).
[Crossref]

Lougovski, P.

B. Qi, P. Lougovski, R. Pooser, W. Grice, and M. Bobrek, “Generating the local oscillator” locally” in continuous-variable quantum key distribution based on coherent detection,” arXiv preprint arXiv:1503.00662 (2015).

Ma, X.-C.

X.-C. Ma, S.-H. Sun, M.-S. Jiang, and L.-M. Liang, “Wavelength attack on practical continuous-variable quantum-key-distribution system with a heterodyne protocol,” Phys. Rev. A 87, 052309 (2013).
[Crossref]

Madsen, L. S.

L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3, 1083 (2012).
[Crossref] [PubMed]

McLaughlin, S. W.

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and et al., “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76, 042305 (2007).
[Crossref]

Mitchell, M.

N. Behbood, F. M. Ciurana, G. Colangelo, M. Napolitano, G. Tóth, R. Sewell, and M. Mitchell, “Generation of macroscopic singlet states in a cold atomic ensemble,” Phys. Rev. Lett. 113, 093601 (2014).
[Crossref] [PubMed]

Mitchell, M. W.

G. Tóth and M. W. Mitchell, “Generation of macroscopic singlet states in atomic ensembles,” New J. Phys. 12, 053007 (2010).
[Crossref]

Napolitano, M.

N. Behbood, F. M. Ciurana, G. Colangelo, M. Napolitano, G. Tóth, R. Sewell, and M. Mitchell, “Generation of macroscopic singlet states in a cold atomic ensemble,” Phys. Rev. Lett. 113, 093601 (2014).
[Crossref] [PubMed]

Navascués, M.

M. Navascués, F. Grosshans, and A. Acin, “Optimality of gaussian attacks in continuous-variable quantum cryptography,” Phys. Rev. Lett. 97, 190502 (2006).
[Crossref] [PubMed]

Polzik, E.

J. Hald, J. Sørensen, C. Schori, and E. Polzik, “Spin squeezed atoms: a macroscopic entangled ensemble created by light,” Phys. Rev. Lett. 83, 1319 (1999).
[Crossref]

Polzik, E. S.

G. Vasilakis, H. Shen, K. Jensen, M. Balabas, D. Salart, B. Chen, and E. S. Polzik, “Generation of a squeezed state of an oscillator by stroboscopic back-action-evading measurement,” Nat. Phys. 11, 389–392 (2015).
[Crossref]

T. Fernholz, H. Krauter, K. Jensen, J. F. Sherson, A. S. Sørensen, and E. S. Polzik, “Spin squeezing of atomic ensembles via nuclear-electronic spin entanglement,” Phys. Rev. Lett. 101, 073601 (2008).
[Crossref] [PubMed]

N. J. Cerf, G. Leuchs, and E. S. Polzik, Quantum Information with Continuous Variables of Atoms and Light (Imperial College Press, 2007).

Pooser, R.

B. Qi, P. Lougovski, R. Pooser, W. Grice, and M. Bobrek, “Generating the local oscillator” locally” in continuous-variable quantum key distribution based on coherent detection,” arXiv preprint arXiv:1503.00662 (2015).

Qi, B.

B. Qi, P. Lougovski, R. Pooser, W. Grice, and M. Bobrek, “Generating the local oscillator” locally” in continuous-variable quantum key distribution based on coherent detection,” arXiv preprint arXiv:1503.00662 (2015).

Raymer, M.

Ribordy, G.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145 (2002).
[Crossref]

Ruppert, L.

V. C. Usenko, L. Ruppert, and R. Filip, “Entanglement-based continuous-variable quantum key distribution with multimode states and detectors,” Phys. Rev. A 90, 062326 (2014).
[Crossref]

Salart, D.

G. Vasilakis, H. Shen, K. Jensen, M. Balabas, D. Salart, B. Chen, and E. S. Polzik, “Generation of a squeezed state of an oscillator by stroboscopic back-action-evading measurement,” Nat. Phys. 11, 389–392 (2015).
[Crossref]

Schori, C.

J. Hald, J. Sørensen, C. Schori, and E. Polzik, “Spin squeezed atoms: a macroscopic entangled ensemble created by light,” Phys. Rev. Lett. 83, 1319 (1999).
[Crossref]

Sewell, R.

N. Behbood, F. M. Ciurana, G. Colangelo, M. Napolitano, G. Tóth, R. Sewell, and M. Mitchell, “Generation of macroscopic singlet states in a cold atomic ensemble,” Phys. Rev. Lett. 113, 093601 (2014).
[Crossref] [PubMed]

Shen, H.

G. Vasilakis, H. Shen, K. Jensen, M. Balabas, D. Salart, B. Chen, and E. S. Polzik, “Generation of a squeezed state of an oscillator by stroboscopic back-action-evading measurement,” Nat. Phys. 11, 389–392 (2015).
[Crossref]

Sherson, J. F.

T. Fernholz, H. Krauter, K. Jensen, J. F. Sherson, A. S. Sørensen, and E. S. Polzik, “Spin squeezing of atomic ensembles via nuclear-electronic spin entanglement,” Phys. Rev. Lett. 101, 073601 (2008).
[Crossref] [PubMed]

Smithey, D.

Sørensen, A. S.

T. Fernholz, H. Krauter, K. Jensen, J. F. Sherson, A. S. Sørensen, and E. S. Polzik, “Spin squeezing of atomic ensembles via nuclear-electronic spin entanglement,” Phys. Rev. Lett. 101, 073601 (2008).
[Crossref] [PubMed]

Sørensen, J.

J. Hald, J. Sørensen, C. Schori, and E. Polzik, “Spin squeezed atoms: a macroscopic entangled ensemble created by light,” Phys. Rev. Lett. 83, 1319 (1999).
[Crossref]

Sun, S.-H.

X.-C. Ma, S.-H. Sun, M.-S. Jiang, and L.-M. Liang, “Wavelength attack on practical continuous-variable quantum-key-distribution system with a heterodyne protocol,” Phys. Rev. A 87, 052309 (2013).
[Crossref]

Tittel, W.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145 (2002).
[Crossref]

Tóth, G.

N. Behbood, F. M. Ciurana, G. Colangelo, M. Napolitano, G. Tóth, R. Sewell, and M. Mitchell, “Generation of macroscopic singlet states in a cold atomic ensemble,” Phys. Rev. Lett. 113, 093601 (2014).
[Crossref] [PubMed]

G. Tóth and M. W. Mitchell, “Generation of macroscopic singlet states in atomic ensembles,” New J. Phys. 12, 053007 (2010).
[Crossref]

Tualle-Brouri, R.

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and et al., “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76, 042305 (2007).
[Crossref]

F. Grosshans, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and P. Grangier, “Virtual entanglement and reconciliation protocols for quantum cryptography with continuous variables,” Quantum Info. Comput. 3, 535–552 (2003).

Usenko, V. C.

V. C. Usenko, L. Ruppert, and R. Filip, “Entanglement-based continuous-variable quantum key distribution with multimode states and detectors,” Phys. Rev. A 90, 062326 (2014).
[Crossref]

L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3, 1083 (2012).
[Crossref] [PubMed]

Van Assche, G.

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using gaussian-modulated coherent states,” Nature 421, 238–241 (2003).
[Crossref] [PubMed]

Van Loock, P.

S. L. Braunstein and P. Van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513 (2005).
[Crossref]

Vasilakis, G.

G. Vasilakis, H. Shen, K. Jensen, M. Balabas, D. Salart, B. Chen, and E. S. Polzik, “Generation of a squeezed state of an oscillator by stroboscopic back-action-evading measurement,” Nat. Phys. 11, 389–392 (2015).
[Crossref]

Vasilyev, M.

M. Vasilyev, S.-K. Choi, P. Kumar, and G. M. D’Ariano, “Tomographic measurement of joint photon statistics of the twin-beam quantum state,” Phys. Rev. Lett. 84, 2354 (2000).
[Crossref] [PubMed]

Vidal, G.

G. Vidal and R. F. Werner, “Computable measure of entanglement,” Phys. Rev. A 65, 032314 (2002).
[Crossref]

Wang, S.

J.-Z. Huang, S. Kunz-Jacques, P. Jouguet, C. Weedbrook, Z.-Q. Yin, S. Wang, W. Chen, G.-C. Guo, and Z.-F. Han, “Quantum hacking on quantum key distribution using homodyne detection,” Phys. Rev. A 89, 032304 (2014).
[Crossref]

J.-Z. Huang, C. Weedbrook, Z.-Q. Yin, S. Wang, H.-W. Li, W. Chen, G.-C. Guo, and Z.-F. Han, “Quantum hacking of a continuous-variable quantum-key-distribution system using a wavelength attack,” Phys. Rev. A 87, 062329 (2013).
[Crossref]

Weedbrook, C.

J.-Z. Huang, S. Kunz-Jacques, P. Jouguet, C. Weedbrook, Z.-Q. Yin, S. Wang, W. Chen, G.-C. Guo, and Z.-F. Han, “Quantum hacking on quantum key distribution using homodyne detection,” Phys. Rev. A 89, 032304 (2014).
[Crossref]

J.-Z. Huang, C. Weedbrook, Z.-Q. Yin, S. Wang, H.-W. Li, W. Chen, G.-C. Guo, and Z.-F. Han, “Quantum hacking of a continuous-variable quantum-key-distribution system using a wavelength attack,” Phys. Rev. A 87, 062329 (2013).
[Crossref]

Wenger, J.

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using gaussian-modulated coherent states,” Nature 421, 238–241 (2003).
[Crossref] [PubMed]

F. Grosshans, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and P. Grangier, “Virtual entanglement and reconciliation protocols for quantum cryptography with continuous variables,” Quantum Info. Comput. 3, 535–552 (2003).

Werner, R. F.

G. Vidal and R. F. Werner, “Computable measure of entanglement,” Phys. Rev. A 65, 032314 (2002).
[Crossref]

Wolf, M. M.

M. M. Wolf, G. Giedke, and J. I. Cirac, “Extremality of gaussian quantum states,” Phys. Rev. Lett. 96, 080502 (2006).
[Crossref] [PubMed]

Yin, Z.-Q.

J.-Z. Huang, S. Kunz-Jacques, P. Jouguet, C. Weedbrook, Z.-Q. Yin, S. Wang, W. Chen, G.-C. Guo, and Z.-F. Han, “Quantum hacking on quantum key distribution using homodyne detection,” Phys. Rev. A 89, 032304 (2014).
[Crossref]

J.-Z. Huang, C. Weedbrook, Z.-Q. Yin, S. Wang, H.-W. Li, W. Chen, G.-C. Guo, and Z.-F. Han, “Quantum hacking of a continuous-variable quantum-key-distribution system using a wavelength attack,” Phys. Rev. A 87, 062329 (2013).
[Crossref]

Zbinden, H.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145 (2002).
[Crossref]

J. Mod. Opt. (1)

M. Collett, R. Loudon, and C. Gardiner, “Quantum theory of optical homodyne and heterodyne detection,” J. Mod. Opt. 34, 881–902 (1987).
[Crossref]

J. Opt. Soc. Am. B (1)

Nat. Commun. (1)

L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3, 1083 (2012).
[Crossref] [PubMed]

Nat. Phys. (1)

G. Vasilakis, H. Shen, K. Jensen, M. Balabas, D. Salart, B. Chen, and E. S. Polzik, “Generation of a squeezed state of an oscillator by stroboscopic back-action-evading measurement,” Nat. Phys. 11, 389–392 (2015).
[Crossref]

Nature (1)

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using gaussian-modulated coherent states,” Nature 421, 238–241 (2003).
[Crossref] [PubMed]

New J. Phys. (1)

G. Tóth and M. W. Mitchell, “Generation of macroscopic singlet states in atomic ensembles,” New J. Phys. 12, 053007 (2010).
[Crossref]

Phys. Rev. A (7)

V. C. Usenko, L. Ruppert, and R. Filip, “Entanglement-based continuous-variable quantum key distribution with multimode states and detectors,” Phys. Rev. A 90, 062326 (2014).
[Crossref]

G. Vidal and R. F. Werner, “Computable measure of entanglement,” Phys. Rev. A 65, 032314 (2002).
[Crossref]

X.-C. Ma, S.-H. Sun, M.-S. Jiang, and L.-M. Liang, “Wavelength attack on practical continuous-variable quantum-key-distribution system with a heterodyne protocol,” Phys. Rev. A 87, 052309 (2013).
[Crossref]

J.-Z. Huang, C. Weedbrook, Z.-Q. Yin, S. Wang, H.-W. Li, W. Chen, G.-C. Guo, and Z.-F. Han, “Quantum hacking of a continuous-variable quantum-key-distribution system using a wavelength attack,” Phys. Rev. A 87, 062329 (2013).
[Crossref]

J.-Z. Huang, S. Kunz-Jacques, P. Jouguet, C. Weedbrook, Z.-Q. Yin, S. Wang, W. Chen, G.-C. Guo, and Z.-F. Han, “Quantum hacking on quantum key distribution using homodyne detection,” Phys. Rev. A 89, 032304 (2014).
[Crossref]

P. Jouguet, S. Kunz-Jacques, and A. Leverrier, “Long-distance continuous-variable quantum key distribution with a gaussian modulation,” Phys. Rev. A 84, 062317 (2011).
[Crossref]

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and et al., “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76, 042305 (2007).
[Crossref]

Phys. Rev. Lett. (9)

M. Vasilyev, S.-K. Choi, P. Kumar, and G. M. D’Ariano, “Tomographic measurement of joint photon statistics of the twin-beam quantum state,” Phys. Rev. Lett. 84, 2354 (2000).
[Crossref] [PubMed]

T. S. Iskhakov, I. N. Agafonov, M. V. Chekhova, and G. Leuchs, “Polarization-entangled light pulses of 10 5 photons,” Phys. Rev. Lett. 109, 150502 (2012).
[Crossref]

N. Behbood, F. M. Ciurana, G. Colangelo, M. Napolitano, G. Tóth, R. Sewell, and M. Mitchell, “Generation of macroscopic singlet states in a cold atomic ensemble,” Phys. Rev. Lett. 113, 093601 (2014).
[Crossref] [PubMed]

J. Hald, J. Sørensen, C. Schori, and E. Polzik, “Spin squeezed atoms: a macroscopic entangled ensemble created by light,” Phys. Rev. Lett. 83, 1319 (1999).
[Crossref]

T. Fernholz, H. Krauter, K. Jensen, J. F. Sherson, A. S. Sørensen, and E. S. Polzik, “Spin squeezing of atomic ensembles via nuclear-electronic spin entanglement,” Phys. Rev. Lett. 101, 073601 (2008).
[Crossref] [PubMed]

T. Iskhakov, M. V. Chekhova, and G. Leuchs, “Generation and direct detection of broadband mesoscopic polarization-squeezed vacuum,” Phys. Rev. Lett. 102, 183602 (2009).
[Crossref] [PubMed]

M. M. Wolf, G. Giedke, and J. I. Cirac, “Extremality of gaussian quantum states,” Phys. Rev. Lett. 96, 080502 (2006).
[Crossref] [PubMed]

M. Navascués, F. Grosshans, and A. Acin, “Optimality of gaussian attacks in continuous-variable quantum cryptography,” Phys. Rev. Lett. 97, 190502 (2006).
[Crossref] [PubMed]

R. Garcia-Patron and N. J. Cerf, “Unconditional optimality of gaussian attacks against continuous-variable quantum key distribution,” Phys. Rev. Lett. 97, 190503 (2006).
[Crossref] [PubMed]

Quantum Info. Comput. (1)

F. Grosshans, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and P. Grangier, “Virtual entanglement and reconciliation protocols for quantum cryptography with continuous variables,” Quantum Info. Comput. 3, 535–552 (2003).

Rev. Mod. Phys. (2)

S. L. Braunstein and P. Van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513 (2005).
[Crossref]

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145 (2002).
[Crossref]

Other (2)

B. Qi, P. Lougovski, R. Pooser, W. Grice, and M. Bobrek, “Generating the local oscillator” locally” in continuous-variable quantum key distribution based on coherent detection,” arXiv preprint arXiv:1503.00662 (2015).

N. J. Cerf, G. Leuchs, and E. S. Polzik, Quantum Information with Continuous Variables of Atoms and Light (Imperial College Press, 2007).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Homodyne detection of macroscopic bright multimode states of light. Matched M signal modes aSi are coupled to LO modes aLOi and unmatched N signal modes bSj are coupled to respective vacuum modes bSj on a generally unbalanced beamsplitter with transmittances Tai and Tbj for modes a and b respectively. The quadrature measurement consists in detecting the photocurrent difference between the two photodetectors on the output ports of the coupling beamsplitter.

Fig. 2
Fig. 2

(Left): Prepare-and-measure and (Right): entanglement-based quantum communication schemes based on the multimode bright squeezed/entangled states and homodyne measurements.

Fig. 3
Fig. 3

(Left): Logarithmic negativity of the macroscopic entangled states measured by the homodyne detectors versus total mean photon number. (Right): Key rate secure against collective attacks in bits per channel use, generated from the homodyne measurement of the macroscopic squeezed states versus total mean number of photons. On both the graphs the total number of modes is 103 and εtot = 10−2 (solid lines), εtot = 0.1 (red dashed lines). Channel transmittance (from bottom to top) η = 0.1, 0.5, 0.9, channel noise is absent.

Fig. 4
Fig. 4

Key rate secure against collective attacks in bits per channel use, generated from the homodyne measurement of the macroscopic squeezed states plotted with respect to the channel transmittance η (in negative dB scale) in the presence of channel noise χ = 5% SNU and upon εtot = 0.1. (Left): No detection unbalancing, perfect post-processing efficiency β = 1 (black solid lines) and reduced efficiency β = 0.97 (red dashed lines), = 103, 102, 10 (from left to right). (Right): Reduced post-processing efficiency β = 0.97, no unbalancing (black solid line), unbalanced detection of the signal Ta = 1/2 + 1% (blue dashed line), additional unbalanced detection of the unmatched modes Tb = 1/2 − 1% (red dot-dashed line).

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

( a S i a LO i ) out = ( T a i 1 T a i 1 T a i T a i ) ( a S i a LO i ) ,
n 1 = i M [ T a i a S i a S i + T a i ( 1 T a i ) ( a S i a LO i + a LO i a S i ) + ( 1 T a i ) a LO i a LO i ] + + ε j N [ T b j b S j b S j + T b j ( 1 T b j ) ( b S j b V j + b V j b S j ) + ( 1 T b j ) b V j b B j ]
n 2 = i M [ ( 1 T a i ) a S i a S i T a i ( 1 T a i ) ( a S i a LO i + a LO i a S i ) + T a i a LO i a LO i ] + + ε j N [ ( 1 T b j ) b S j b S j T b j ( 1 T b j ) ( b S j b V j + b V j b S j ) + T b j b V j b B j ] .
Δ i = α i M x i + ε j N ( b S j b V j + b V j b S j ) .
Var ( Δ i ) norm = Var ( X ) + ε tot 2 n ¯ ,
ε tot 2 = N ε 2 M α 2 .
Var ( Δ i ) norm ( unb ) = Var ( X ) + ε tot 2 T a ( 1 T a ) [ T b ( 1 T b ) n ¯ + ( T b T a ) 2 Var ( n ) ] ,
K = β I AB χ B E ,

Metrics