Abstract

Linear optical quantum gates have been proposed as a possible implementation for quantum computers. Most experimental linear optical quantum gates are constructed with free-space optical components with negligible loss. In this work, we analyze symmetric and asymmetric partially polarizing lossy beam splitters. Using the generalized beam splitter equations, we study the effects of loss on two linear optical quantum gates: the first is a commonly used CNOT gate, and the second is a W state expansion gate. Envisioning inherent loss in plasmonics and metamaterials as a new degree of freedom and those materials systems as a route for miniaturization, we reconsider the requirements of the lossy CNOT gate and show it is possible to simplify the three-beam-splitter design to a single beam splitter without sacrificing success probability.

© 2021 Optical Society of America

Full Article  |  PDF Article
More Like This
Logic-qubit controlled-NOT gate of decoherence-free subspace with nonlinear quantum optics

Chun-Yan Li, Zu-Rong Zhang, Shi-Hai Sun, Mu-Sheng Jiang, and Lin-Mei Liang
J. Opt. Soc. Am. B 30(7) 1872-1877 (2013)

Heralded high-fidelity quantum hyper-CNOT gates assisted by charged quantum dots inside single-sided optical microcavities

Yu-Hong Han, Cong Cao, Ling Fan, and Ru Zhang
Opt. Express 29(13) 20045-20062 (2021)

References

  • View by:

  1. A. Gueddana, P. Gholami, and V. Lakshminarayanan, “Can a universal quantum cloner be used to design an experimentally feasible near-deterministic CNOT gate?” Quantum Inf. Process. 18, 221 (2019).
    [Crossref]
  2. M. A. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2010).
  3. E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
    [Crossref]
  4. T. C. Ralph, A. Hayes, and A. Gilchrist, “Loss-tolerant optical qubits,” Phys. Rev. Lett. 95, 100501 (2005).
    [Crossref]
  5. P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135 (2007).
    [Crossref]
  6. M. Koashi, T. Yamamoto, and N. Imoto, “Probabilistic manipulation of entangled photons,” Phys. Rev. A 63, 030301 (2001).
    [Crossref]
  7. T. Pittman, B. Jacobs, and J. Franson, “Probabilistic quantum logic operations using polarizing beam splitters,” Phys. Rev. A 64, 062311 (2001).
    [Crossref]
  8. T. Ralph, A. White, W. Munro, and G. Milburn, “Simple scheme for efficient linear optics quantum gates,” Phys. Rev. A 65, 012314 (2001).
    [Crossref]
  9. M. A. Nielsen, “Optical quantum computation using cluster states,” Phys. Rev. Lett. 93, 040503 (2004).
    [Crossref]
  10. H. F. Hofmann and S. Takeuchi, “Quantum phase gate for photonic qubits using only beam splitters and postselection,” Phys. Rev. A 66, 024308 (2002).
    [Crossref]
  11. N. Kiesel, C. Schmid, U. Weber, R. Ursin, and H. Weinfurter, “Linear optics controlled-phase gate made simple,” Phys. Rev. Lett. 95, 210505 (2005).
    [Crossref]
  12. T. Pittman, M. Fitch, B. Jacobs, and J. Franson, “Experimental controlled-NOT logic gate for single photons in the coincidence basis,” Phys. Rev. A 68, 032316 (2003).
    [Crossref]
  13. Z. Zhao, A.-N. Zhang, Y.-A. Chen, H. Zhang, J.-F. Du, T. Yang, and J.-W. Pan, “Experimental demonstration of a nondestructive controlled-not quantum gate for two independent photon qubits,” Phys. Rev. Lett. 94, 030501 (2005).
    [Crossref]
  14. J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, “Demonstration of an all-optical quantum controlled-NOT gate,” Nature 426, 264–267 (2003).
    [Crossref]
  15. S. Gasparoni, J.-W. Pan, P. Walther, T. Rudolph, and A. Zeilinger, “Realization of a photonic controlled-NOT gate sufficient for quantum computation,” Phys. Rev. Lett. 93, 020504 (2004).
    [Crossref]
  16. X.-H. Bao, T.-Y. Chen, Q. Zhang, J. Yang, H. Zhang, T. Yang, and J.-W. Pan, “Optical nondestructive controlled-NOT gate without using entangled photons,” Phys. Rev. Lett. 98, 170502 (2007).
    [Crossref]
  17. T. C. Ralph, N. K. Langford, T. Bell, and A. White, “Linear optical controlled-NOT gate in the coincidence basis,” Phys. Rev. A 65, 062324 (2002).
    [Crossref]
  18. R. Okamoto, H. F. Hofmann, S. Takeuchi, and K. Sasaki, “Demonstration of an optical quantum controlled-NOT gate without path interference,” Phys. Rev. Lett. 95, 210506 (2005).
    [Crossref]
  19. J. Chen, J. B. Altepeter, M. Medic, K. F. Lee, B. Gokden, R. H. Hadfield, S. W. Nam, and P. Kumar, “Demonstration of a quantum controlled-NOT gate in the telecommunications band,” Phys. Rev. Lett. 100, 133603 (2008).
    [Crossref]
  20. N. K. Langford, T. Weinhold, R. Prevedel, K. Resch, A. Gilchrist, J. O’Brien, G. Pryde, and A. White, “Demonstration of a simple entangling optical gate and its use in Bell-state analysis,” Phys. Rev. Lett. 95, 210504 (2005).
    [Crossref]
  21. A. S. Clark, J. Fulconis, J. G. Rarity, W. J. Wadsworth, and J. L. O’Brien, “All-optical-fiber polarization-based quantum logic gate,” Phys. Rev. A 79, 030303 (2009).
    [Crossref]
  22. B. P. Lanyon, T. J. Weinhold, N. K. Langford, M. Barbieri, D. F. James, A. Gilchrist, and A. G. White, “Experimental demonstration of a compiled version of Shor’s algorithm with quantum entanglement,” Phys. Rev. Lett. 99, 250505 (2007).
    [Crossref]
  23. J. L. O’Brien, G. Pryde, A. Gilchrist, D. James, N. K. Langford, T. Ralph, and A. White, “Quantum process tomography of a controlled-NOT gate,” Phys. Rev. Lett. 93, 080502 (2004).
    [Crossref]
  24. P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
    [Crossref]
  25. Z.-S. Yuan, Y.-A. Chen, B. Zhao, S. Chen, J. Schmiedmayer, and J.-W. Pan, “Experimental demonstration of a BDCZ quantum repeater node,” Nature 454, 1098–1101 (2008).
    [Crossref]
  26. B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
    [Crossref]
  27. K. Sanaka, K. Kawahara, and T. Kuga, “Experimental probabilistic manipulation of down-converted photon pairs using unbalanced interferometers,” Phys. Rev. A 66, 040301 (2002).
    [Crossref]
  28. T. Pittman, B. Jacobs, and J. Franson, “Demonstration of nondeterministic quantum logic operations using linear optical elements,” Phys. Rev. Lett. 88, 257902 (2002).
    [Crossref]
  29. X. Qiang, X. Zhou, J. Wang, C. M. Wilkes, T. Loke, S. O’Gara, L. Kling, G. D. Marshall, R. Santagati, T. C. Ralph, and J. B. Wang, “Large-scale silicon quantum photonics implementing arbitrary two-qubit processing,” Nat. Photonics 12, 534–539 (2018).
    [Crossref]
  30. X. Zhang, J. E. Davis, and D. Ö. Güney, “Ultra-thin metamaterial beam splitters,” Appl. Sci. 10, 53 (2020).
    [Crossref]
  31. S. Wang, Q. Cheng, Y. Gong, P. Xu, C. Sun, L. Li, T. Li, and S. Zhu, “A 14×14 µm2 footprint polarization-encoded quantum controlled-NOT gate based on hybrid waveguide,” Nat. Commun. 7, 11490 (2016).
    [Crossref]
  32. R. Uppu, T. A. Wolterink, T. B. Tentrup, and P. W. Pinkse, “Quantum optics of lossy asymmetric beam splitters,” Opt. Express 24, 16440–16449 (2016).
    [Crossref]
  33. B. Vest, M.-C. Dheur, É. Devaux, A. Baron, E. Rousseau, J.-P. Hugonin, J.-J. Greffet, G. Messin, and F. Marquier, “Anti-coalescence of bosons on a lossy beam splitter,” Science 356, 1373–1376 (2017).
    [Crossref]
  34. J. Jeffers, “Interference and the lossless lossy beam splitter,” J. Mod. Opt. 47, 1819–1824 (2000).
    [Crossref]
  35. S. M. Barnett, J. Jeffers, A. Gatti, and R. Loudon, “Quantum optics of lossy beam splitters,” Phys. Rev. A 57, 2134–2145 (1998).
    [Crossref]
  36. M. A. Al Farooqui, J. Breeland, M. I. Aslam, M. Sadatgol, Ş. K. Özdemir, M. Tame, L. Yang, and D. Ö. Güney, “Quantum entanglement distillation with metamaterials,” Opt. Express 23, 17941–17954 (2015).
    [Crossref]
  37. M. Asano, M. Bechu, M. Tame, Ş. K. Özdemir, R. Ikuta, D. Ö. Güney, T. Yamamoto, L. Yang, M. Wegener, and N. Imoto, “Distillation of photon entanglement using a plasmonic metamaterial,” Sci. Rep. 5, 18313 (2015).
    [Crossref]
  38. A. Vora, J. Gwamuri, N. Pala, A. Kulkarni, J. M. Pearce, and D. Ö. Güney, “Exchanging Ohmic losses in metamaterial absorbers with useful optical absorption for photovoltaics,” Sci. Rep. 4, 4901 (2014).
    [Crossref]
  39. P. Tuong, J. Park, V. Lam, W. Jang, S. Nikitov, and Y. Lee, “Dielectric and Ohmic losses in perfectly absorbing metamaterials,” Opt. Commun. 295, 17–20 (2013).
    [Crossref]
  40. A. Ü. Hardal and M. Wubs, “Quantum coherent absorption of squeezed light,” Optica 6, 181–189 (2019).
    [Crossref]
  41. P. Kok, “Creating large NOON states with imperfect phase control,” Opt. Spectrosc. 111, 520–522 (2011).
    [Crossref]
  42. P. M. Alsing, E. E. Hach, C. C. Tison, and A. M. Smith, “Quantum-optical description of losses in ring resonators based on field-operator transformations,” Phys. Rev. A 95, 053828 (2017).
    [Crossref]
  43. T. Tashima, Ş. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Local expansion of photonic W state using a polarization-dependent beamsplitter,” New J. Phys. 11, 023024 (2009).
    [Crossref]
  44. Y.-S. Zhou, F. Wang, and M.-X. Luo, “Efficient superdense coding with W states,” Int. J. Theor. Phys. 57, 1935–1941 (2018).
    [Crossref]
  45. X. Yang, M.-Q. Bai, and Z.-W. Mo, “Controlled dense coding with the W state,” Int. J. Theor. Phys. 56, 3525–3533 (2017).
    [Crossref]
  46. K. Li, F.-Z. Kong, M. Yang, F. Ozaydin, Q. Yang, and Z.-L. Cao, “Generating multi-photon W-like states for perfect quantum teleportation and superdense coding,” Quantum Inf. Process. 15, 3137–3150 (2016).
    [Crossref]
  47. B.-S. Shi and A. Tomita, “Teleportation of an unknown state by W state,” Phys. Lett. A 296, 161–164 (2002).
    [Crossref]
  48. X. Xiao-Ming, D. Li, G. Ya-Jun, and C. Feng, “Quantum teleportation schemes of an N-particle state via three-particle general W states,” Commun. Theor. Phys. 49, 905 (2008).
    [Crossref]
  49. H.-J. Cao and H.-S. Song, “Quantum secure direct communication scheme using a W state and teleportation,” Phys. Scripta 74, 572 (2006).
    [Crossref]
  50. W. Jian, Z. Quan, and T. Chao-Jing, “Quantum secure communication scheme with W state,” Commun. Theor. Phys. 48, 637 (2007).
    [Crossref]
  51. D. Li, X. Xiao-Ming, G. Ya-Jun, and C. Feng, “Improvement on quantum secure direct communication with W state in noisy channel,” Commun. Theor. Phys. 51, 232 (2009).
    [Crossref]
  52. A. Zeilinger, “General properties of lossless beam splitters in interferometry,” Am. J. Phys. 49, 882–883 (1981).
    [Crossref]

2020 (1)

X. Zhang, J. E. Davis, and D. Ö. Güney, “Ultra-thin metamaterial beam splitters,” Appl. Sci. 10, 53 (2020).
[Crossref]

2019 (2)

A. Gueddana, P. Gholami, and V. Lakshminarayanan, “Can a universal quantum cloner be used to design an experimentally feasible near-deterministic CNOT gate?” Quantum Inf. Process. 18, 221 (2019).
[Crossref]

A. Ü. Hardal and M. Wubs, “Quantum coherent absorption of squeezed light,” Optica 6, 181–189 (2019).
[Crossref]

2018 (2)

Y.-S. Zhou, F. Wang, and M.-X. Luo, “Efficient superdense coding with W states,” Int. J. Theor. Phys. 57, 1935–1941 (2018).
[Crossref]

X. Qiang, X. Zhou, J. Wang, C. M. Wilkes, T. Loke, S. O’Gara, L. Kling, G. D. Marshall, R. Santagati, T. C. Ralph, and J. B. Wang, “Large-scale silicon quantum photonics implementing arbitrary two-qubit processing,” Nat. Photonics 12, 534–539 (2018).
[Crossref]

2017 (3)

X. Yang, M.-Q. Bai, and Z.-W. Mo, “Controlled dense coding with the W state,” Int. J. Theor. Phys. 56, 3525–3533 (2017).
[Crossref]

B. Vest, M.-C. Dheur, É. Devaux, A. Baron, E. Rousseau, J.-P. Hugonin, J.-J. Greffet, G. Messin, and F. Marquier, “Anti-coalescence of bosons on a lossy beam splitter,” Science 356, 1373–1376 (2017).
[Crossref]

P. M. Alsing, E. E. Hach, C. C. Tison, and A. M. Smith, “Quantum-optical description of losses in ring resonators based on field-operator transformations,” Phys. Rev. A 95, 053828 (2017).
[Crossref]

2016 (3)

K. Li, F.-Z. Kong, M. Yang, F. Ozaydin, Q. Yang, and Z.-L. Cao, “Generating multi-photon W-like states for perfect quantum teleportation and superdense coding,” Quantum Inf. Process. 15, 3137–3150 (2016).
[Crossref]

S. Wang, Q. Cheng, Y. Gong, P. Xu, C. Sun, L. Li, T. Li, and S. Zhu, “A 14×14 µm2 footprint polarization-encoded quantum controlled-NOT gate based on hybrid waveguide,” Nat. Commun. 7, 11490 (2016).
[Crossref]

R. Uppu, T. A. Wolterink, T. B. Tentrup, and P. W. Pinkse, “Quantum optics of lossy asymmetric beam splitters,” Opt. Express 24, 16440–16449 (2016).
[Crossref]

2015 (2)

M. A. Al Farooqui, J. Breeland, M. I. Aslam, M. Sadatgol, Ş. K. Özdemir, M. Tame, L. Yang, and D. Ö. Güney, “Quantum entanglement distillation with metamaterials,” Opt. Express 23, 17941–17954 (2015).
[Crossref]

M. Asano, M. Bechu, M. Tame, Ş. K. Özdemir, R. Ikuta, D. Ö. Güney, T. Yamamoto, L. Yang, M. Wegener, and N. Imoto, “Distillation of photon entanglement using a plasmonic metamaterial,” Sci. Rep. 5, 18313 (2015).
[Crossref]

2014 (1)

A. Vora, J. Gwamuri, N. Pala, A. Kulkarni, J. M. Pearce, and D. Ö. Güney, “Exchanging Ohmic losses in metamaterial absorbers with useful optical absorption for photovoltaics,” Sci. Rep. 4, 4901 (2014).
[Crossref]

2013 (1)

P. Tuong, J. Park, V. Lam, W. Jang, S. Nikitov, and Y. Lee, “Dielectric and Ohmic losses in perfectly absorbing metamaterials,” Opt. Commun. 295, 17–20 (2013).
[Crossref]

2011 (1)

P. Kok, “Creating large NOON states with imperfect phase control,” Opt. Spectrosc. 111, 520–522 (2011).
[Crossref]

2009 (4)

T. Tashima, Ş. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Local expansion of photonic W state using a polarization-dependent beamsplitter,” New J. Phys. 11, 023024 (2009).
[Crossref]

D. Li, X. Xiao-Ming, G. Ya-Jun, and C. Feng, “Improvement on quantum secure direct communication with W state in noisy channel,” Commun. Theor. Phys. 51, 232 (2009).
[Crossref]

A. S. Clark, J. Fulconis, J. G. Rarity, W. J. Wadsworth, and J. L. O’Brien, “All-optical-fiber polarization-based quantum logic gate,” Phys. Rev. A 79, 030303 (2009).
[Crossref]

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[Crossref]

2008 (3)

J. Chen, J. B. Altepeter, M. Medic, K. F. Lee, B. Gokden, R. H. Hadfield, S. W. Nam, and P. Kumar, “Demonstration of a quantum controlled-NOT gate in the telecommunications band,” Phys. Rev. Lett. 100, 133603 (2008).
[Crossref]

Z.-S. Yuan, Y.-A. Chen, B. Zhao, S. Chen, J. Schmiedmayer, and J.-W. Pan, “Experimental demonstration of a BDCZ quantum repeater node,” Nature 454, 1098–1101 (2008).
[Crossref]

X. Xiao-Ming, D. Li, G. Ya-Jun, and C. Feng, “Quantum teleportation schemes of an N-particle state via three-particle general W states,” Commun. Theor. Phys. 49, 905 (2008).
[Crossref]

2007 (4)

W. Jian, Z. Quan, and T. Chao-Jing, “Quantum secure communication scheme with W state,” Commun. Theor. Phys. 48, 637 (2007).
[Crossref]

B. P. Lanyon, T. J. Weinhold, N. K. Langford, M. Barbieri, D. F. James, A. Gilchrist, and A. G. White, “Experimental demonstration of a compiled version of Shor’s algorithm with quantum entanglement,” Phys. Rev. Lett. 99, 250505 (2007).
[Crossref]

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135 (2007).
[Crossref]

X.-H. Bao, T.-Y. Chen, Q. Zhang, J. Yang, H. Zhang, T. Yang, and J.-W. Pan, “Optical nondestructive controlled-NOT gate without using entangled photons,” Phys. Rev. Lett. 98, 170502 (2007).
[Crossref]

2006 (1)

H.-J. Cao and H.-S. Song, “Quantum secure direct communication scheme using a W state and teleportation,” Phys. Scripta 74, 572 (2006).
[Crossref]

2005 (6)

T. C. Ralph, A. Hayes, and A. Gilchrist, “Loss-tolerant optical qubits,” Phys. Rev. Lett. 95, 100501 (2005).
[Crossref]

N. Kiesel, C. Schmid, U. Weber, R. Ursin, and H. Weinfurter, “Linear optics controlled-phase gate made simple,” Phys. Rev. Lett. 95, 210505 (2005).
[Crossref]

Z. Zhao, A.-N. Zhang, Y.-A. Chen, H. Zhang, J.-F. Du, T. Yang, and J.-W. Pan, “Experimental demonstration of a nondestructive controlled-not quantum gate for two independent photon qubits,” Phys. Rev. Lett. 94, 030501 (2005).
[Crossref]

N. K. Langford, T. Weinhold, R. Prevedel, K. Resch, A. Gilchrist, J. O’Brien, G. Pryde, and A. White, “Demonstration of a simple entangling optical gate and its use in Bell-state analysis,” Phys. Rev. Lett. 95, 210504 (2005).
[Crossref]

R. Okamoto, H. F. Hofmann, S. Takeuchi, and K. Sasaki, “Demonstration of an optical quantum controlled-NOT gate without path interference,” Phys. Rev. Lett. 95, 210506 (2005).
[Crossref]

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
[Crossref]

2004 (3)

J. L. O’Brien, G. Pryde, A. Gilchrist, D. James, N. K. Langford, T. Ralph, and A. White, “Quantum process tomography of a controlled-NOT gate,” Phys. Rev. Lett. 93, 080502 (2004).
[Crossref]

S. Gasparoni, J.-W. Pan, P. Walther, T. Rudolph, and A. Zeilinger, “Realization of a photonic controlled-NOT gate sufficient for quantum computation,” Phys. Rev. Lett. 93, 020504 (2004).
[Crossref]

M. A. Nielsen, “Optical quantum computation using cluster states,” Phys. Rev. Lett. 93, 040503 (2004).
[Crossref]

2003 (2)

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, “Demonstration of an all-optical quantum controlled-NOT gate,” Nature 426, 264–267 (2003).
[Crossref]

T. Pittman, M. Fitch, B. Jacobs, and J. Franson, “Experimental controlled-NOT logic gate for single photons in the coincidence basis,” Phys. Rev. A 68, 032316 (2003).
[Crossref]

2002 (5)

T. C. Ralph, N. K. Langford, T. Bell, and A. White, “Linear optical controlled-NOT gate in the coincidence basis,” Phys. Rev. A 65, 062324 (2002).
[Crossref]

H. F. Hofmann and S. Takeuchi, “Quantum phase gate for photonic qubits using only beam splitters and postselection,” Phys. Rev. A 66, 024308 (2002).
[Crossref]

K. Sanaka, K. Kawahara, and T. Kuga, “Experimental probabilistic manipulation of down-converted photon pairs using unbalanced interferometers,” Phys. Rev. A 66, 040301 (2002).
[Crossref]

T. Pittman, B. Jacobs, and J. Franson, “Demonstration of nondeterministic quantum logic operations using linear optical elements,” Phys. Rev. Lett. 88, 257902 (2002).
[Crossref]

B.-S. Shi and A. Tomita, “Teleportation of an unknown state by W state,” Phys. Lett. A 296, 161–164 (2002).
[Crossref]

2001 (4)

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[Crossref]

M. Koashi, T. Yamamoto, and N. Imoto, “Probabilistic manipulation of entangled photons,” Phys. Rev. A 63, 030301 (2001).
[Crossref]

T. Pittman, B. Jacobs, and J. Franson, “Probabilistic quantum logic operations using polarizing beam splitters,” Phys. Rev. A 64, 062311 (2001).
[Crossref]

T. Ralph, A. White, W. Munro, and G. Milburn, “Simple scheme for efficient linear optics quantum gates,” Phys. Rev. A 65, 012314 (2001).
[Crossref]

2000 (1)

J. Jeffers, “Interference and the lossless lossy beam splitter,” J. Mod. Opt. 47, 1819–1824 (2000).
[Crossref]

1998 (1)

S. M. Barnett, J. Jeffers, A. Gatti, and R. Loudon, “Quantum optics of lossy beam splitters,” Phys. Rev. A 57, 2134–2145 (1998).
[Crossref]

1981 (1)

A. Zeilinger, “General properties of lossless beam splitters in interferometry,” Am. J. Phys. 49, 882–883 (1981).
[Crossref]

Al Farooqui, M. A.

Almeida, M. P.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[Crossref]

Alsing, P. M.

P. M. Alsing, E. E. Hach, C. C. Tison, and A. M. Smith, “Quantum-optical description of losses in ring resonators based on field-operator transformations,” Phys. Rev. A 95, 053828 (2017).
[Crossref]

Altepeter, J. B.

J. Chen, J. B. Altepeter, M. Medic, K. F. Lee, B. Gokden, R. H. Hadfield, S. W. Nam, and P. Kumar, “Demonstration of a quantum controlled-NOT gate in the telecommunications band,” Phys. Rev. Lett. 100, 133603 (2008).
[Crossref]

Asano, M.

M. Asano, M. Bechu, M. Tame, Ş. K. Özdemir, R. Ikuta, D. Ö. Güney, T. Yamamoto, L. Yang, M. Wegener, and N. Imoto, “Distillation of photon entanglement using a plasmonic metamaterial,” Sci. Rep. 5, 18313 (2015).
[Crossref]

Aslam, M. I.

Aspelmeyer, M.

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
[Crossref]

Bai, M.-Q.

X. Yang, M.-Q. Bai, and Z.-W. Mo, “Controlled dense coding with the W state,” Int. J. Theor. Phys. 56, 3525–3533 (2017).
[Crossref]

Bao, X.-H.

X.-H. Bao, T.-Y. Chen, Q. Zhang, J. Yang, H. Zhang, T. Yang, and J.-W. Pan, “Optical nondestructive controlled-NOT gate without using entangled photons,” Phys. Rev. Lett. 98, 170502 (2007).
[Crossref]

Barbieri, M.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[Crossref]

B. P. Lanyon, T. J. Weinhold, N. K. Langford, M. Barbieri, D. F. James, A. Gilchrist, and A. G. White, “Experimental demonstration of a compiled version of Shor’s algorithm with quantum entanglement,” Phys. Rev. Lett. 99, 250505 (2007).
[Crossref]

Barnett, S. M.

S. M. Barnett, J. Jeffers, A. Gatti, and R. Loudon, “Quantum optics of lossy beam splitters,” Phys. Rev. A 57, 2134–2145 (1998).
[Crossref]

Baron, A.

B. Vest, M.-C. Dheur, É. Devaux, A. Baron, E. Rousseau, J.-P. Hugonin, J.-J. Greffet, G. Messin, and F. Marquier, “Anti-coalescence of bosons on a lossy beam splitter,” Science 356, 1373–1376 (2017).
[Crossref]

Bechu, M.

M. Asano, M. Bechu, M. Tame, Ş. K. Özdemir, R. Ikuta, D. Ö. Güney, T. Yamamoto, L. Yang, M. Wegener, and N. Imoto, “Distillation of photon entanglement using a plasmonic metamaterial,” Sci. Rep. 5, 18313 (2015).
[Crossref]

Bell, T.

T. C. Ralph, N. K. Langford, T. Bell, and A. White, “Linear optical controlled-NOT gate in the coincidence basis,” Phys. Rev. A 65, 062324 (2002).
[Crossref]

Branning, D.

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, “Demonstration of an all-optical quantum controlled-NOT gate,” Nature 426, 264–267 (2003).
[Crossref]

Breeland, J.

Cao, H.-J.

H.-J. Cao and H.-S. Song, “Quantum secure direct communication scheme using a W state and teleportation,” Phys. Scripta 74, 572 (2006).
[Crossref]

Cao, Z.-L.

K. Li, F.-Z. Kong, M. Yang, F. Ozaydin, Q. Yang, and Z.-L. Cao, “Generating multi-photon W-like states for perfect quantum teleportation and superdense coding,” Quantum Inf. Process. 15, 3137–3150 (2016).
[Crossref]

Chao-Jing, T.

W. Jian, Z. Quan, and T. Chao-Jing, “Quantum secure communication scheme with W state,” Commun. Theor. Phys. 48, 637 (2007).
[Crossref]

Chen, J.

J. Chen, J. B. Altepeter, M. Medic, K. F. Lee, B. Gokden, R. H. Hadfield, S. W. Nam, and P. Kumar, “Demonstration of a quantum controlled-NOT gate in the telecommunications band,” Phys. Rev. Lett. 100, 133603 (2008).
[Crossref]

Chen, S.

Z.-S. Yuan, Y.-A. Chen, B. Zhao, S. Chen, J. Schmiedmayer, and J.-W. Pan, “Experimental demonstration of a BDCZ quantum repeater node,” Nature 454, 1098–1101 (2008).
[Crossref]

Chen, T.-Y.

X.-H. Bao, T.-Y. Chen, Q. Zhang, J. Yang, H. Zhang, T. Yang, and J.-W. Pan, “Optical nondestructive controlled-NOT gate without using entangled photons,” Phys. Rev. Lett. 98, 170502 (2007).
[Crossref]

Chen, Y.-A.

Z.-S. Yuan, Y.-A. Chen, B. Zhao, S. Chen, J. Schmiedmayer, and J.-W. Pan, “Experimental demonstration of a BDCZ quantum repeater node,” Nature 454, 1098–1101 (2008).
[Crossref]

Z. Zhao, A.-N. Zhang, Y.-A. Chen, H. Zhang, J.-F. Du, T. Yang, and J.-W. Pan, “Experimental demonstration of a nondestructive controlled-not quantum gate for two independent photon qubits,” Phys. Rev. Lett. 94, 030501 (2005).
[Crossref]

Cheng, Q.

S. Wang, Q. Cheng, Y. Gong, P. Xu, C. Sun, L. Li, T. Li, and S. Zhu, “A 14×14 µm2 footprint polarization-encoded quantum controlled-NOT gate based on hybrid waveguide,” Nat. Commun. 7, 11490 (2016).
[Crossref]

Chuang, I.

M. A. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2010).

Clark, A. S.

A. S. Clark, J. Fulconis, J. G. Rarity, W. J. Wadsworth, and J. L. O’Brien, “All-optical-fiber polarization-based quantum logic gate,” Phys. Rev. A 79, 030303 (2009).
[Crossref]

Davis, J. E.

X. Zhang, J. E. Davis, and D. Ö. Güney, “Ultra-thin metamaterial beam splitters,” Appl. Sci. 10, 53 (2020).
[Crossref]

Devaux, É.

B. Vest, M.-C. Dheur, É. Devaux, A. Baron, E. Rousseau, J.-P. Hugonin, J.-J. Greffet, G. Messin, and F. Marquier, “Anti-coalescence of bosons on a lossy beam splitter,” Science 356, 1373–1376 (2017).
[Crossref]

Dheur, M.-C.

B. Vest, M.-C. Dheur, É. Devaux, A. Baron, E. Rousseau, J.-P. Hugonin, J.-J. Greffet, G. Messin, and F. Marquier, “Anti-coalescence of bosons on a lossy beam splitter,” Science 356, 1373–1376 (2017).
[Crossref]

Dowling, J. P.

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135 (2007).
[Crossref]

Du, J.-F.

Z. Zhao, A.-N. Zhang, Y.-A. Chen, H. Zhang, J.-F. Du, T. Yang, and J.-W. Pan, “Experimental demonstration of a nondestructive controlled-not quantum gate for two independent photon qubits,” Phys. Rev. Lett. 94, 030501 (2005).
[Crossref]

Feng, C.

D. Li, X. Xiao-Ming, G. Ya-Jun, and C. Feng, “Improvement on quantum secure direct communication with W state in noisy channel,” Commun. Theor. Phys. 51, 232 (2009).
[Crossref]

X. Xiao-Ming, D. Li, G. Ya-Jun, and C. Feng, “Quantum teleportation schemes of an N-particle state via three-particle general W states,” Commun. Theor. Phys. 49, 905 (2008).
[Crossref]

Fitch, M.

T. Pittman, M. Fitch, B. Jacobs, and J. Franson, “Experimental controlled-NOT logic gate for single photons in the coincidence basis,” Phys. Rev. A 68, 032316 (2003).
[Crossref]

Franson, J.

T. Pittman, M. Fitch, B. Jacobs, and J. Franson, “Experimental controlled-NOT logic gate for single photons in the coincidence basis,” Phys. Rev. A 68, 032316 (2003).
[Crossref]

T. Pittman, B. Jacobs, and J. Franson, “Demonstration of nondeterministic quantum logic operations using linear optical elements,” Phys. Rev. Lett. 88, 257902 (2002).
[Crossref]

T. Pittman, B. Jacobs, and J. Franson, “Probabilistic quantum logic operations using polarizing beam splitters,” Phys. Rev. A 64, 062311 (2001).
[Crossref]

Fulconis, J.

A. S. Clark, J. Fulconis, J. G. Rarity, W. J. Wadsworth, and J. L. O’Brien, “All-optical-fiber polarization-based quantum logic gate,” Phys. Rev. A 79, 030303 (2009).
[Crossref]

Gasparoni, S.

S. Gasparoni, J.-W. Pan, P. Walther, T. Rudolph, and A. Zeilinger, “Realization of a photonic controlled-NOT gate sufficient for quantum computation,” Phys. Rev. Lett. 93, 020504 (2004).
[Crossref]

Gatti, A.

S. M. Barnett, J. Jeffers, A. Gatti, and R. Loudon, “Quantum optics of lossy beam splitters,” Phys. Rev. A 57, 2134–2145 (1998).
[Crossref]

Gholami, P.

A. Gueddana, P. Gholami, and V. Lakshminarayanan, “Can a universal quantum cloner be used to design an experimentally feasible near-deterministic CNOT gate?” Quantum Inf. Process. 18, 221 (2019).
[Crossref]

Gilchrist, A.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[Crossref]

B. P. Lanyon, T. J. Weinhold, N. K. Langford, M. Barbieri, D. F. James, A. Gilchrist, and A. G. White, “Experimental demonstration of a compiled version of Shor’s algorithm with quantum entanglement,” Phys. Rev. Lett. 99, 250505 (2007).
[Crossref]

N. K. Langford, T. Weinhold, R. Prevedel, K. Resch, A. Gilchrist, J. O’Brien, G. Pryde, and A. White, “Demonstration of a simple entangling optical gate and its use in Bell-state analysis,” Phys. Rev. Lett. 95, 210504 (2005).
[Crossref]

T. C. Ralph, A. Hayes, and A. Gilchrist, “Loss-tolerant optical qubits,” Phys. Rev. Lett. 95, 100501 (2005).
[Crossref]

J. L. O’Brien, G. Pryde, A. Gilchrist, D. James, N. K. Langford, T. Ralph, and A. White, “Quantum process tomography of a controlled-NOT gate,” Phys. Rev. Lett. 93, 080502 (2004).
[Crossref]

Gokden, B.

J. Chen, J. B. Altepeter, M. Medic, K. F. Lee, B. Gokden, R. H. Hadfield, S. W. Nam, and P. Kumar, “Demonstration of a quantum controlled-NOT gate in the telecommunications band,” Phys. Rev. Lett. 100, 133603 (2008).
[Crossref]

Gong, Y.

S. Wang, Q. Cheng, Y. Gong, P. Xu, C. Sun, L. Li, T. Li, and S. Zhu, “A 14×14 µm2 footprint polarization-encoded quantum controlled-NOT gate based on hybrid waveguide,” Nat. Commun. 7, 11490 (2016).
[Crossref]

Greffet, J.-J.

B. Vest, M.-C. Dheur, É. Devaux, A. Baron, E. Rousseau, J.-P. Hugonin, J.-J. Greffet, G. Messin, and F. Marquier, “Anti-coalescence of bosons on a lossy beam splitter,” Science 356, 1373–1376 (2017).
[Crossref]

Gueddana, A.

A. Gueddana, P. Gholami, and V. Lakshminarayanan, “Can a universal quantum cloner be used to design an experimentally feasible near-deterministic CNOT gate?” Quantum Inf. Process. 18, 221 (2019).
[Crossref]

Güney, D. Ö.

X. Zhang, J. E. Davis, and D. Ö. Güney, “Ultra-thin metamaterial beam splitters,” Appl. Sci. 10, 53 (2020).
[Crossref]

M. A. Al Farooqui, J. Breeland, M. I. Aslam, M. Sadatgol, Ş. K. Özdemir, M. Tame, L. Yang, and D. Ö. Güney, “Quantum entanglement distillation with metamaterials,” Opt. Express 23, 17941–17954 (2015).
[Crossref]

M. Asano, M. Bechu, M. Tame, Ş. K. Özdemir, R. Ikuta, D. Ö. Güney, T. Yamamoto, L. Yang, M. Wegener, and N. Imoto, “Distillation of photon entanglement using a plasmonic metamaterial,” Sci. Rep. 5, 18313 (2015).
[Crossref]

A. Vora, J. Gwamuri, N. Pala, A. Kulkarni, J. M. Pearce, and D. Ö. Güney, “Exchanging Ohmic losses in metamaterial absorbers with useful optical absorption for photovoltaics,” Sci. Rep. 4, 4901 (2014).
[Crossref]

Gwamuri, J.

A. Vora, J. Gwamuri, N. Pala, A. Kulkarni, J. M. Pearce, and D. Ö. Güney, “Exchanging Ohmic losses in metamaterial absorbers with useful optical absorption for photovoltaics,” Sci. Rep. 4, 4901 (2014).
[Crossref]

Hach, E. E.

P. M. Alsing, E. E. Hach, C. C. Tison, and A. M. Smith, “Quantum-optical description of losses in ring resonators based on field-operator transformations,” Phys. Rev. A 95, 053828 (2017).
[Crossref]

Hadfield, R. H.

J. Chen, J. B. Altepeter, M. Medic, K. F. Lee, B. Gokden, R. H. Hadfield, S. W. Nam, and P. Kumar, “Demonstration of a quantum controlled-NOT gate in the telecommunications band,” Phys. Rev. Lett. 100, 133603 (2008).
[Crossref]

Hardal, A. Ü.

Hayes, A.

T. C. Ralph, A. Hayes, and A. Gilchrist, “Loss-tolerant optical qubits,” Phys. Rev. Lett. 95, 100501 (2005).
[Crossref]

Hofmann, H. F.

R. Okamoto, H. F. Hofmann, S. Takeuchi, and K. Sasaki, “Demonstration of an optical quantum controlled-NOT gate without path interference,” Phys. Rev. Lett. 95, 210506 (2005).
[Crossref]

H. F. Hofmann and S. Takeuchi, “Quantum phase gate for photonic qubits using only beam splitters and postselection,” Phys. Rev. A 66, 024308 (2002).
[Crossref]

Hugonin, J.-P.

B. Vest, M.-C. Dheur, É. Devaux, A. Baron, E. Rousseau, J.-P. Hugonin, J.-J. Greffet, G. Messin, and F. Marquier, “Anti-coalescence of bosons on a lossy beam splitter,” Science 356, 1373–1376 (2017).
[Crossref]

Ikuta, R.

M. Asano, M. Bechu, M. Tame, Ş. K. Özdemir, R. Ikuta, D. Ö. Güney, T. Yamamoto, L. Yang, M. Wegener, and N. Imoto, “Distillation of photon entanglement using a plasmonic metamaterial,” Sci. Rep. 5, 18313 (2015).
[Crossref]

Imoto, N.

M. Asano, M. Bechu, M. Tame, Ş. K. Özdemir, R. Ikuta, D. Ö. Güney, T. Yamamoto, L. Yang, M. Wegener, and N. Imoto, “Distillation of photon entanglement using a plasmonic metamaterial,” Sci. Rep. 5, 18313 (2015).
[Crossref]

T. Tashima, Ş. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Local expansion of photonic W state using a polarization-dependent beamsplitter,” New J. Phys. 11, 023024 (2009).
[Crossref]

M. Koashi, T. Yamamoto, and N. Imoto, “Probabilistic manipulation of entangled photons,” Phys. Rev. A 63, 030301 (2001).
[Crossref]

Jacobs, B.

T. Pittman, M. Fitch, B. Jacobs, and J. Franson, “Experimental controlled-NOT logic gate for single photons in the coincidence basis,” Phys. Rev. A 68, 032316 (2003).
[Crossref]

T. Pittman, B. Jacobs, and J. Franson, “Demonstration of nondeterministic quantum logic operations using linear optical elements,” Phys. Rev. Lett. 88, 257902 (2002).
[Crossref]

T. Pittman, B. Jacobs, and J. Franson, “Probabilistic quantum logic operations using polarizing beam splitters,” Phys. Rev. A 64, 062311 (2001).
[Crossref]

James, D.

J. L. O’Brien, G. Pryde, A. Gilchrist, D. James, N. K. Langford, T. Ralph, and A. White, “Quantum process tomography of a controlled-NOT gate,” Phys. Rev. Lett. 93, 080502 (2004).
[Crossref]

James, D. F.

B. P. Lanyon, T. J. Weinhold, N. K. Langford, M. Barbieri, D. F. James, A. Gilchrist, and A. G. White, “Experimental demonstration of a compiled version of Shor’s algorithm with quantum entanglement,” Phys. Rev. Lett. 99, 250505 (2007).
[Crossref]

Jang, W.

P. Tuong, J. Park, V. Lam, W. Jang, S. Nikitov, and Y. Lee, “Dielectric and Ohmic losses in perfectly absorbing metamaterials,” Opt. Commun. 295, 17–20 (2013).
[Crossref]

Jeffers, J.

J. Jeffers, “Interference and the lossless lossy beam splitter,” J. Mod. Opt. 47, 1819–1824 (2000).
[Crossref]

S. M. Barnett, J. Jeffers, A. Gatti, and R. Loudon, “Quantum optics of lossy beam splitters,” Phys. Rev. A 57, 2134–2145 (1998).
[Crossref]

Jennewein, T.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[Crossref]

Jian, W.

W. Jian, Z. Quan, and T. Chao-Jing, “Quantum secure communication scheme with W state,” Commun. Theor. Phys. 48, 637 (2007).
[Crossref]

Kawahara, K.

K. Sanaka, K. Kawahara, and T. Kuga, “Experimental probabilistic manipulation of down-converted photon pairs using unbalanced interferometers,” Phys. Rev. A 66, 040301 (2002).
[Crossref]

Kiesel, N.

N. Kiesel, C. Schmid, U. Weber, R. Ursin, and H. Weinfurter, “Linear optics controlled-phase gate made simple,” Phys. Rev. Lett. 95, 210505 (2005).
[Crossref]

Kling, L.

X. Qiang, X. Zhou, J. Wang, C. M. Wilkes, T. Loke, S. O’Gara, L. Kling, G. D. Marshall, R. Santagati, T. C. Ralph, and J. B. Wang, “Large-scale silicon quantum photonics implementing arbitrary two-qubit processing,” Nat. Photonics 12, 534–539 (2018).
[Crossref]

Knill, E.

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[Crossref]

Koashi, M.

T. Tashima, Ş. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Local expansion of photonic W state using a polarization-dependent beamsplitter,” New J. Phys. 11, 023024 (2009).
[Crossref]

M. Koashi, T. Yamamoto, and N. Imoto, “Probabilistic manipulation of entangled photons,” Phys. Rev. A 63, 030301 (2001).
[Crossref]

Kok, P.

P. Kok, “Creating large NOON states with imperfect phase control,” Opt. Spectrosc. 111, 520–522 (2011).
[Crossref]

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135 (2007).
[Crossref]

Kong, F.-Z.

K. Li, F.-Z. Kong, M. Yang, F. Ozaydin, Q. Yang, and Z.-L. Cao, “Generating multi-photon W-like states for perfect quantum teleportation and superdense coding,” Quantum Inf. Process. 15, 3137–3150 (2016).
[Crossref]

Kuga, T.

K. Sanaka, K. Kawahara, and T. Kuga, “Experimental probabilistic manipulation of down-converted photon pairs using unbalanced interferometers,” Phys. Rev. A 66, 040301 (2002).
[Crossref]

Kulkarni, A.

A. Vora, J. Gwamuri, N. Pala, A. Kulkarni, J. M. Pearce, and D. Ö. Güney, “Exchanging Ohmic losses in metamaterial absorbers with useful optical absorption for photovoltaics,” Sci. Rep. 4, 4901 (2014).
[Crossref]

Kumar, P.

J. Chen, J. B. Altepeter, M. Medic, K. F. Lee, B. Gokden, R. H. Hadfield, S. W. Nam, and P. Kumar, “Demonstration of a quantum controlled-NOT gate in the telecommunications band,” Phys. Rev. Lett. 100, 133603 (2008).
[Crossref]

Laflamme, R.

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[Crossref]

Lakshminarayanan, V.

A. Gueddana, P. Gholami, and V. Lakshminarayanan, “Can a universal quantum cloner be used to design an experimentally feasible near-deterministic CNOT gate?” Quantum Inf. Process. 18, 221 (2019).
[Crossref]

Lam, V.

P. Tuong, J. Park, V. Lam, W. Jang, S. Nikitov, and Y. Lee, “Dielectric and Ohmic losses in perfectly absorbing metamaterials,” Opt. Commun. 295, 17–20 (2013).
[Crossref]

Langford, N. K.

B. P. Lanyon, T. J. Weinhold, N. K. Langford, M. Barbieri, D. F. James, A. Gilchrist, and A. G. White, “Experimental demonstration of a compiled version of Shor’s algorithm with quantum entanglement,” Phys. Rev. Lett. 99, 250505 (2007).
[Crossref]

N. K. Langford, T. Weinhold, R. Prevedel, K. Resch, A. Gilchrist, J. O’Brien, G. Pryde, and A. White, “Demonstration of a simple entangling optical gate and its use in Bell-state analysis,” Phys. Rev. Lett. 95, 210504 (2005).
[Crossref]

J. L. O’Brien, G. Pryde, A. Gilchrist, D. James, N. K. Langford, T. Ralph, and A. White, “Quantum process tomography of a controlled-NOT gate,” Phys. Rev. Lett. 93, 080502 (2004).
[Crossref]

T. C. Ralph, N. K. Langford, T. Bell, and A. White, “Linear optical controlled-NOT gate in the coincidence basis,” Phys. Rev. A 65, 062324 (2002).
[Crossref]

Lanyon, B. P.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[Crossref]

B. P. Lanyon, T. J. Weinhold, N. K. Langford, M. Barbieri, D. F. James, A. Gilchrist, and A. G. White, “Experimental demonstration of a compiled version of Shor’s algorithm with quantum entanglement,” Phys. Rev. Lett. 99, 250505 (2007).
[Crossref]

Lee, K. F.

J. Chen, J. B. Altepeter, M. Medic, K. F. Lee, B. Gokden, R. H. Hadfield, S. W. Nam, and P. Kumar, “Demonstration of a quantum controlled-NOT gate in the telecommunications band,” Phys. Rev. Lett. 100, 133603 (2008).
[Crossref]

Lee, Y.

P. Tuong, J. Park, V. Lam, W. Jang, S. Nikitov, and Y. Lee, “Dielectric and Ohmic losses in perfectly absorbing metamaterials,” Opt. Commun. 295, 17–20 (2013).
[Crossref]

Li, D.

D. Li, X. Xiao-Ming, G. Ya-Jun, and C. Feng, “Improvement on quantum secure direct communication with W state in noisy channel,” Commun. Theor. Phys. 51, 232 (2009).
[Crossref]

X. Xiao-Ming, D. Li, G. Ya-Jun, and C. Feng, “Quantum teleportation schemes of an N-particle state via three-particle general W states,” Commun. Theor. Phys. 49, 905 (2008).
[Crossref]

Li, K.

K. Li, F.-Z. Kong, M. Yang, F. Ozaydin, Q. Yang, and Z.-L. Cao, “Generating multi-photon W-like states for perfect quantum teleportation and superdense coding,” Quantum Inf. Process. 15, 3137–3150 (2016).
[Crossref]

Li, L.

S. Wang, Q. Cheng, Y. Gong, P. Xu, C. Sun, L. Li, T. Li, and S. Zhu, “A 14×14 µm2 footprint polarization-encoded quantum controlled-NOT gate based on hybrid waveguide,” Nat. Commun. 7, 11490 (2016).
[Crossref]

Li, T.

S. Wang, Q. Cheng, Y. Gong, P. Xu, C. Sun, L. Li, T. Li, and S. Zhu, “A 14×14 µm2 footprint polarization-encoded quantum controlled-NOT gate based on hybrid waveguide,” Nat. Commun. 7, 11490 (2016).
[Crossref]

Loke, T.

X. Qiang, X. Zhou, J. Wang, C. M. Wilkes, T. Loke, S. O’Gara, L. Kling, G. D. Marshall, R. Santagati, T. C. Ralph, and J. B. Wang, “Large-scale silicon quantum photonics implementing arbitrary two-qubit processing,” Nat. Photonics 12, 534–539 (2018).
[Crossref]

Loudon, R.

S. M. Barnett, J. Jeffers, A. Gatti, and R. Loudon, “Quantum optics of lossy beam splitters,” Phys. Rev. A 57, 2134–2145 (1998).
[Crossref]

Luo, M.-X.

Y.-S. Zhou, F. Wang, and M.-X. Luo, “Efficient superdense coding with W states,” Int. J. Theor. Phys. 57, 1935–1941 (2018).
[Crossref]

Marquier, F.

B. Vest, M.-C. Dheur, É. Devaux, A. Baron, E. Rousseau, J.-P. Hugonin, J.-J. Greffet, G. Messin, and F. Marquier, “Anti-coalescence of bosons on a lossy beam splitter,” Science 356, 1373–1376 (2017).
[Crossref]

Marshall, G. D.

X. Qiang, X. Zhou, J. Wang, C. M. Wilkes, T. Loke, S. O’Gara, L. Kling, G. D. Marshall, R. Santagati, T. C. Ralph, and J. B. Wang, “Large-scale silicon quantum photonics implementing arbitrary two-qubit processing,” Nat. Photonics 12, 534–539 (2018).
[Crossref]

Medic, M.

J. Chen, J. B. Altepeter, M. Medic, K. F. Lee, B. Gokden, R. H. Hadfield, S. W. Nam, and P. Kumar, “Demonstration of a quantum controlled-NOT gate in the telecommunications band,” Phys. Rev. Lett. 100, 133603 (2008).
[Crossref]

Messin, G.

B. Vest, M.-C. Dheur, É. Devaux, A. Baron, E. Rousseau, J.-P. Hugonin, J.-J. Greffet, G. Messin, and F. Marquier, “Anti-coalescence of bosons on a lossy beam splitter,” Science 356, 1373–1376 (2017).
[Crossref]

Milburn, G.

T. Ralph, A. White, W. Munro, and G. Milburn, “Simple scheme for efficient linear optics quantum gates,” Phys. Rev. A 65, 012314 (2001).
[Crossref]

Milburn, G. J.

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135 (2007).
[Crossref]

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[Crossref]

Mo, Z.-W.

X. Yang, M.-Q. Bai, and Z.-W. Mo, “Controlled dense coding with the W state,” Int. J. Theor. Phys. 56, 3525–3533 (2017).
[Crossref]

Munro, W.

T. Ralph, A. White, W. Munro, and G. Milburn, “Simple scheme for efficient linear optics quantum gates,” Phys. Rev. A 65, 012314 (2001).
[Crossref]

Munro, W. J.

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135 (2007).
[Crossref]

Nam, S. W.

J. Chen, J. B. Altepeter, M. Medic, K. F. Lee, B. Gokden, R. H. Hadfield, S. W. Nam, and P. Kumar, “Demonstration of a quantum controlled-NOT gate in the telecommunications band,” Phys. Rev. Lett. 100, 133603 (2008).
[Crossref]

Nemoto, K.

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135 (2007).
[Crossref]

Nielsen, M. A.

M. A. Nielsen, “Optical quantum computation using cluster states,” Phys. Rev. Lett. 93, 040503 (2004).
[Crossref]

M. A. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2010).

Nikitov, S.

P. Tuong, J. Park, V. Lam, W. Jang, S. Nikitov, and Y. Lee, “Dielectric and Ohmic losses in perfectly absorbing metamaterials,” Opt. Commun. 295, 17–20 (2013).
[Crossref]

O’Brien, J.

N. K. Langford, T. Weinhold, R. Prevedel, K. Resch, A. Gilchrist, J. O’Brien, G. Pryde, and A. White, “Demonstration of a simple entangling optical gate and its use in Bell-state analysis,” Phys. Rev. Lett. 95, 210504 (2005).
[Crossref]

O’Brien, J. L.

A. S. Clark, J. Fulconis, J. G. Rarity, W. J. Wadsworth, and J. L. O’Brien, “All-optical-fiber polarization-based quantum logic gate,” Phys. Rev. A 79, 030303 (2009).
[Crossref]

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[Crossref]

J. L. O’Brien, G. Pryde, A. Gilchrist, D. James, N. K. Langford, T. Ralph, and A. White, “Quantum process tomography of a controlled-NOT gate,” Phys. Rev. Lett. 93, 080502 (2004).
[Crossref]

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, “Demonstration of an all-optical quantum controlled-NOT gate,” Nature 426, 264–267 (2003).
[Crossref]

O’Gara, S.

X. Qiang, X. Zhou, J. Wang, C. M. Wilkes, T. Loke, S. O’Gara, L. Kling, G. D. Marshall, R. Santagati, T. C. Ralph, and J. B. Wang, “Large-scale silicon quantum photonics implementing arbitrary two-qubit processing,” Nat. Photonics 12, 534–539 (2018).
[Crossref]

Okamoto, R.

R. Okamoto, H. F. Hofmann, S. Takeuchi, and K. Sasaki, “Demonstration of an optical quantum controlled-NOT gate without path interference,” Phys. Rev. Lett. 95, 210506 (2005).
[Crossref]

Ozaydin, F.

K. Li, F.-Z. Kong, M. Yang, F. Ozaydin, Q. Yang, and Z.-L. Cao, “Generating multi-photon W-like states for perfect quantum teleportation and superdense coding,” Quantum Inf. Process. 15, 3137–3150 (2016).
[Crossref]

Özdemir, S. K.

M. A. Al Farooqui, J. Breeland, M. I. Aslam, M. Sadatgol, Ş. K. Özdemir, M. Tame, L. Yang, and D. Ö. Güney, “Quantum entanglement distillation with metamaterials,” Opt. Express 23, 17941–17954 (2015).
[Crossref]

M. Asano, M. Bechu, M. Tame, Ş. K. Özdemir, R. Ikuta, D. Ö. Güney, T. Yamamoto, L. Yang, M. Wegener, and N. Imoto, “Distillation of photon entanglement using a plasmonic metamaterial,” Sci. Rep. 5, 18313 (2015).
[Crossref]

T. Tashima, Ş. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Local expansion of photonic W state using a polarization-dependent beamsplitter,” New J. Phys. 11, 023024 (2009).
[Crossref]

Pala, N.

A. Vora, J. Gwamuri, N. Pala, A. Kulkarni, J. M. Pearce, and D. Ö. Güney, “Exchanging Ohmic losses in metamaterial absorbers with useful optical absorption for photovoltaics,” Sci. Rep. 4, 4901 (2014).
[Crossref]

Pan, J.-W.

Z.-S. Yuan, Y.-A. Chen, B. Zhao, S. Chen, J. Schmiedmayer, and J.-W. Pan, “Experimental demonstration of a BDCZ quantum repeater node,” Nature 454, 1098–1101 (2008).
[Crossref]

X.-H. Bao, T.-Y. Chen, Q. Zhang, J. Yang, H. Zhang, T. Yang, and J.-W. Pan, “Optical nondestructive controlled-NOT gate without using entangled photons,” Phys. Rev. Lett. 98, 170502 (2007).
[Crossref]

Z. Zhao, A.-N. Zhang, Y.-A. Chen, H. Zhang, J.-F. Du, T. Yang, and J.-W. Pan, “Experimental demonstration of a nondestructive controlled-not quantum gate for two independent photon qubits,” Phys. Rev. Lett. 94, 030501 (2005).
[Crossref]

S. Gasparoni, J.-W. Pan, P. Walther, T. Rudolph, and A. Zeilinger, “Realization of a photonic controlled-NOT gate sufficient for quantum computation,” Phys. Rev. Lett. 93, 020504 (2004).
[Crossref]

Park, J.

P. Tuong, J. Park, V. Lam, W. Jang, S. Nikitov, and Y. Lee, “Dielectric and Ohmic losses in perfectly absorbing metamaterials,” Opt. Commun. 295, 17–20 (2013).
[Crossref]

Pearce, J. M.

A. Vora, J. Gwamuri, N. Pala, A. Kulkarni, J. M. Pearce, and D. Ö. Güney, “Exchanging Ohmic losses in metamaterial absorbers with useful optical absorption for photovoltaics,” Sci. Rep. 4, 4901 (2014).
[Crossref]

Pinkse, P. W.

Pittman, T.

T. Pittman, M. Fitch, B. Jacobs, and J. Franson, “Experimental controlled-NOT logic gate for single photons in the coincidence basis,” Phys. Rev. A 68, 032316 (2003).
[Crossref]

T. Pittman, B. Jacobs, and J. Franson, “Demonstration of nondeterministic quantum logic operations using linear optical elements,” Phys. Rev. Lett. 88, 257902 (2002).
[Crossref]

T. Pittman, B. Jacobs, and J. Franson, “Probabilistic quantum logic operations using polarizing beam splitters,” Phys. Rev. A 64, 062311 (2001).
[Crossref]

Prevedel, R.

N. K. Langford, T. Weinhold, R. Prevedel, K. Resch, A. Gilchrist, J. O’Brien, G. Pryde, and A. White, “Demonstration of a simple entangling optical gate and its use in Bell-state analysis,” Phys. Rev. Lett. 95, 210504 (2005).
[Crossref]

Pryde, G.

N. K. Langford, T. Weinhold, R. Prevedel, K. Resch, A. Gilchrist, J. O’Brien, G. Pryde, and A. White, “Demonstration of a simple entangling optical gate and its use in Bell-state analysis,” Phys. Rev. Lett. 95, 210504 (2005).
[Crossref]

J. L. O’Brien, G. Pryde, A. Gilchrist, D. James, N. K. Langford, T. Ralph, and A. White, “Quantum process tomography of a controlled-NOT gate,” Phys. Rev. Lett. 93, 080502 (2004).
[Crossref]

Pryde, G. J.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[Crossref]

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, “Demonstration of an all-optical quantum controlled-NOT gate,” Nature 426, 264–267 (2003).
[Crossref]

Qiang, X.

X. Qiang, X. Zhou, J. Wang, C. M. Wilkes, T. Loke, S. O’Gara, L. Kling, G. D. Marshall, R. Santagati, T. C. Ralph, and J. B. Wang, “Large-scale silicon quantum photonics implementing arbitrary two-qubit processing,” Nat. Photonics 12, 534–539 (2018).
[Crossref]

Quan, Z.

W. Jian, Z. Quan, and T. Chao-Jing, “Quantum secure communication scheme with W state,” Commun. Theor. Phys. 48, 637 (2007).
[Crossref]

Ralph, T.

J. L. O’Brien, G. Pryde, A. Gilchrist, D. James, N. K. Langford, T. Ralph, and A. White, “Quantum process tomography of a controlled-NOT gate,” Phys. Rev. Lett. 93, 080502 (2004).
[Crossref]

T. Ralph, A. White, W. Munro, and G. Milburn, “Simple scheme for efficient linear optics quantum gates,” Phys. Rev. A 65, 012314 (2001).
[Crossref]

Ralph, T. C.

X. Qiang, X. Zhou, J. Wang, C. M. Wilkes, T. Loke, S. O’Gara, L. Kling, G. D. Marshall, R. Santagati, T. C. Ralph, and J. B. Wang, “Large-scale silicon quantum photonics implementing arbitrary two-qubit processing,” Nat. Photonics 12, 534–539 (2018).
[Crossref]

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[Crossref]

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135 (2007).
[Crossref]

T. C. Ralph, A. Hayes, and A. Gilchrist, “Loss-tolerant optical qubits,” Phys. Rev. Lett. 95, 100501 (2005).
[Crossref]

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, “Demonstration of an all-optical quantum controlled-NOT gate,” Nature 426, 264–267 (2003).
[Crossref]

T. C. Ralph, N. K. Langford, T. Bell, and A. White, “Linear optical controlled-NOT gate in the coincidence basis,” Phys. Rev. A 65, 062324 (2002).
[Crossref]

Rarity, J. G.

A. S. Clark, J. Fulconis, J. G. Rarity, W. J. Wadsworth, and J. L. O’Brien, “All-optical-fiber polarization-based quantum logic gate,” Phys. Rev. A 79, 030303 (2009).
[Crossref]

Resch, K.

N. K. Langford, T. Weinhold, R. Prevedel, K. Resch, A. Gilchrist, J. O’Brien, G. Pryde, and A. White, “Demonstration of a simple entangling optical gate and its use in Bell-state analysis,” Phys. Rev. Lett. 95, 210504 (2005).
[Crossref]

Resch, K. J.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[Crossref]

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
[Crossref]

Rousseau, E.

B. Vest, M.-C. Dheur, É. Devaux, A. Baron, E. Rousseau, J.-P. Hugonin, J.-J. Greffet, G. Messin, and F. Marquier, “Anti-coalescence of bosons on a lossy beam splitter,” Science 356, 1373–1376 (2017).
[Crossref]

Rudolph, T.

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
[Crossref]

S. Gasparoni, J.-W. Pan, P. Walther, T. Rudolph, and A. Zeilinger, “Realization of a photonic controlled-NOT gate sufficient for quantum computation,” Phys. Rev. Lett. 93, 020504 (2004).
[Crossref]

Sadatgol, M.

Sanaka, K.

K. Sanaka, K. Kawahara, and T. Kuga, “Experimental probabilistic manipulation of down-converted photon pairs using unbalanced interferometers,” Phys. Rev. A 66, 040301 (2002).
[Crossref]

Santagati, R.

X. Qiang, X. Zhou, J. Wang, C. M. Wilkes, T. Loke, S. O’Gara, L. Kling, G. D. Marshall, R. Santagati, T. C. Ralph, and J. B. Wang, “Large-scale silicon quantum photonics implementing arbitrary two-qubit processing,” Nat. Photonics 12, 534–539 (2018).
[Crossref]

Sasaki, K.

R. Okamoto, H. F. Hofmann, S. Takeuchi, and K. Sasaki, “Demonstration of an optical quantum controlled-NOT gate without path interference,” Phys. Rev. Lett. 95, 210506 (2005).
[Crossref]

Schenck, E.

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
[Crossref]

Schmid, C.

N. Kiesel, C. Schmid, U. Weber, R. Ursin, and H. Weinfurter, “Linear optics controlled-phase gate made simple,” Phys. Rev. Lett. 95, 210505 (2005).
[Crossref]

Schmiedmayer, J.

Z.-S. Yuan, Y.-A. Chen, B. Zhao, S. Chen, J. Schmiedmayer, and J.-W. Pan, “Experimental demonstration of a BDCZ quantum repeater node,” Nature 454, 1098–1101 (2008).
[Crossref]

Shi, B.-S.

B.-S. Shi and A. Tomita, “Teleportation of an unknown state by W state,” Phys. Lett. A 296, 161–164 (2002).
[Crossref]

Smith, A. M.

P. M. Alsing, E. E. Hach, C. C. Tison, and A. M. Smith, “Quantum-optical description of losses in ring resonators based on field-operator transformations,” Phys. Rev. A 95, 053828 (2017).
[Crossref]

Song, H.-S.

H.-J. Cao and H.-S. Song, “Quantum secure direct communication scheme using a W state and teleportation,” Phys. Scripta 74, 572 (2006).
[Crossref]

Sun, C.

S. Wang, Q. Cheng, Y. Gong, P. Xu, C. Sun, L. Li, T. Li, and S. Zhu, “A 14×14 µm2 footprint polarization-encoded quantum controlled-NOT gate based on hybrid waveguide,” Nat. Commun. 7, 11490 (2016).
[Crossref]

Takeuchi, S.

R. Okamoto, H. F. Hofmann, S. Takeuchi, and K. Sasaki, “Demonstration of an optical quantum controlled-NOT gate without path interference,” Phys. Rev. Lett. 95, 210506 (2005).
[Crossref]

H. F. Hofmann and S. Takeuchi, “Quantum phase gate for photonic qubits using only beam splitters and postselection,” Phys. Rev. A 66, 024308 (2002).
[Crossref]

Tame, M.

M. A. Al Farooqui, J. Breeland, M. I. Aslam, M. Sadatgol, Ş. K. Özdemir, M. Tame, L. Yang, and D. Ö. Güney, “Quantum entanglement distillation with metamaterials,” Opt. Express 23, 17941–17954 (2015).
[Crossref]

M. Asano, M. Bechu, M. Tame, Ş. K. Özdemir, R. Ikuta, D. Ö. Güney, T. Yamamoto, L. Yang, M. Wegener, and N. Imoto, “Distillation of photon entanglement using a plasmonic metamaterial,” Sci. Rep. 5, 18313 (2015).
[Crossref]

Tashima, T.

T. Tashima, Ş. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Local expansion of photonic W state using a polarization-dependent beamsplitter,” New J. Phys. 11, 023024 (2009).
[Crossref]

Tentrup, T. B.

Tison, C. C.

P. M. Alsing, E. E. Hach, C. C. Tison, and A. M. Smith, “Quantum-optical description of losses in ring resonators based on field-operator transformations,” Phys. Rev. A 95, 053828 (2017).
[Crossref]

Tomita, A.

B.-S. Shi and A. Tomita, “Teleportation of an unknown state by W state,” Phys. Lett. A 296, 161–164 (2002).
[Crossref]

Tuong, P.

P. Tuong, J. Park, V. Lam, W. Jang, S. Nikitov, and Y. Lee, “Dielectric and Ohmic losses in perfectly absorbing metamaterials,” Opt. Commun. 295, 17–20 (2013).
[Crossref]

Uppu, R.

Ursin, R.

N. Kiesel, C. Schmid, U. Weber, R. Ursin, and H. Weinfurter, “Linear optics controlled-phase gate made simple,” Phys. Rev. Lett. 95, 210505 (2005).
[Crossref]

Vedral, V.

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
[Crossref]

Vest, B.

B. Vest, M.-C. Dheur, É. Devaux, A. Baron, E. Rousseau, J.-P. Hugonin, J.-J. Greffet, G. Messin, and F. Marquier, “Anti-coalescence of bosons on a lossy beam splitter,” Science 356, 1373–1376 (2017).
[Crossref]

Vora, A.

A. Vora, J. Gwamuri, N. Pala, A. Kulkarni, J. M. Pearce, and D. Ö. Güney, “Exchanging Ohmic losses in metamaterial absorbers with useful optical absorption for photovoltaics,” Sci. Rep. 4, 4901 (2014).
[Crossref]

Wadsworth, W. J.

A. S. Clark, J. Fulconis, J. G. Rarity, W. J. Wadsworth, and J. L. O’Brien, “All-optical-fiber polarization-based quantum logic gate,” Phys. Rev. A 79, 030303 (2009).
[Crossref]

Walther, P.

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
[Crossref]

S. Gasparoni, J.-W. Pan, P. Walther, T. Rudolph, and A. Zeilinger, “Realization of a photonic controlled-NOT gate sufficient for quantum computation,” Phys. Rev. Lett. 93, 020504 (2004).
[Crossref]

Wang, F.

Y.-S. Zhou, F. Wang, and M.-X. Luo, “Efficient superdense coding with W states,” Int. J. Theor. Phys. 57, 1935–1941 (2018).
[Crossref]

Wang, J.

X. Qiang, X. Zhou, J. Wang, C. M. Wilkes, T. Loke, S. O’Gara, L. Kling, G. D. Marshall, R. Santagati, T. C. Ralph, and J. B. Wang, “Large-scale silicon quantum photonics implementing arbitrary two-qubit processing,” Nat. Photonics 12, 534–539 (2018).
[Crossref]

Wang, J. B.

X. Qiang, X. Zhou, J. Wang, C. M. Wilkes, T. Loke, S. O’Gara, L. Kling, G. D. Marshall, R. Santagati, T. C. Ralph, and J. B. Wang, “Large-scale silicon quantum photonics implementing arbitrary two-qubit processing,” Nat. Photonics 12, 534–539 (2018).
[Crossref]

Wang, S.

S. Wang, Q. Cheng, Y. Gong, P. Xu, C. Sun, L. Li, T. Li, and S. Zhu, “A 14×14 µm2 footprint polarization-encoded quantum controlled-NOT gate based on hybrid waveguide,” Nat. Commun. 7, 11490 (2016).
[Crossref]

Weber, U.

N. Kiesel, C. Schmid, U. Weber, R. Ursin, and H. Weinfurter, “Linear optics controlled-phase gate made simple,” Phys. Rev. Lett. 95, 210505 (2005).
[Crossref]

Wegener, M.

M. Asano, M. Bechu, M. Tame, Ş. K. Özdemir, R. Ikuta, D. Ö. Güney, T. Yamamoto, L. Yang, M. Wegener, and N. Imoto, “Distillation of photon entanglement using a plasmonic metamaterial,” Sci. Rep. 5, 18313 (2015).
[Crossref]

Weinfurter, H.

N. Kiesel, C. Schmid, U. Weber, R. Ursin, and H. Weinfurter, “Linear optics controlled-phase gate made simple,” Phys. Rev. Lett. 95, 210505 (2005).
[Crossref]

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
[Crossref]

Weinhold, T.

N. K. Langford, T. Weinhold, R. Prevedel, K. Resch, A. Gilchrist, J. O’Brien, G. Pryde, and A. White, “Demonstration of a simple entangling optical gate and its use in Bell-state analysis,” Phys. Rev. Lett. 95, 210504 (2005).
[Crossref]

Weinhold, T. J.

B. P. Lanyon, T. J. Weinhold, N. K. Langford, M. Barbieri, D. F. James, A. Gilchrist, and A. G. White, “Experimental demonstration of a compiled version of Shor’s algorithm with quantum entanglement,” Phys. Rev. Lett. 99, 250505 (2007).
[Crossref]

White, A.

N. K. Langford, T. Weinhold, R. Prevedel, K. Resch, A. Gilchrist, J. O’Brien, G. Pryde, and A. White, “Demonstration of a simple entangling optical gate and its use in Bell-state analysis,” Phys. Rev. Lett. 95, 210504 (2005).
[Crossref]

J. L. O’Brien, G. Pryde, A. Gilchrist, D. James, N. K. Langford, T. Ralph, and A. White, “Quantum process tomography of a controlled-NOT gate,” Phys. Rev. Lett. 93, 080502 (2004).
[Crossref]

T. C. Ralph, N. K. Langford, T. Bell, and A. White, “Linear optical controlled-NOT gate in the coincidence basis,” Phys. Rev. A 65, 062324 (2002).
[Crossref]

T. Ralph, A. White, W. Munro, and G. Milburn, “Simple scheme for efficient linear optics quantum gates,” Phys. Rev. A 65, 012314 (2001).
[Crossref]

White, A. G.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[Crossref]

B. P. Lanyon, T. J. Weinhold, N. K. Langford, M. Barbieri, D. F. James, A. Gilchrist, and A. G. White, “Experimental demonstration of a compiled version of Shor’s algorithm with quantum entanglement,” Phys. Rev. Lett. 99, 250505 (2007).
[Crossref]

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, “Demonstration of an all-optical quantum controlled-NOT gate,” Nature 426, 264–267 (2003).
[Crossref]

Wilkes, C. M.

X. Qiang, X. Zhou, J. Wang, C. M. Wilkes, T. Loke, S. O’Gara, L. Kling, G. D. Marshall, R. Santagati, T. C. Ralph, and J. B. Wang, “Large-scale silicon quantum photonics implementing arbitrary two-qubit processing,” Nat. Photonics 12, 534–539 (2018).
[Crossref]

Wolterink, T. A.

Wubs, M.

Xiao-Ming, X.

D. Li, X. Xiao-Ming, G. Ya-Jun, and C. Feng, “Improvement on quantum secure direct communication with W state in noisy channel,” Commun. Theor. Phys. 51, 232 (2009).
[Crossref]

X. Xiao-Ming, D. Li, G. Ya-Jun, and C. Feng, “Quantum teleportation schemes of an N-particle state via three-particle general W states,” Commun. Theor. Phys. 49, 905 (2008).
[Crossref]

Xu, P.

S. Wang, Q. Cheng, Y. Gong, P. Xu, C. Sun, L. Li, T. Li, and S. Zhu, “A 14×14 µm2 footprint polarization-encoded quantum controlled-NOT gate based on hybrid waveguide,” Nat. Commun. 7, 11490 (2016).
[Crossref]

Ya-Jun, G.

D. Li, X. Xiao-Ming, G. Ya-Jun, and C. Feng, “Improvement on quantum secure direct communication with W state in noisy channel,” Commun. Theor. Phys. 51, 232 (2009).
[Crossref]

X. Xiao-Ming, D. Li, G. Ya-Jun, and C. Feng, “Quantum teleportation schemes of an N-particle state via three-particle general W states,” Commun. Theor. Phys. 49, 905 (2008).
[Crossref]

Yamamoto, T.

M. Asano, M. Bechu, M. Tame, Ş. K. Özdemir, R. Ikuta, D. Ö. Güney, T. Yamamoto, L. Yang, M. Wegener, and N. Imoto, “Distillation of photon entanglement using a plasmonic metamaterial,” Sci. Rep. 5, 18313 (2015).
[Crossref]

T. Tashima, Ş. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Local expansion of photonic W state using a polarization-dependent beamsplitter,” New J. Phys. 11, 023024 (2009).
[Crossref]

M. Koashi, T. Yamamoto, and N. Imoto, “Probabilistic manipulation of entangled photons,” Phys. Rev. A 63, 030301 (2001).
[Crossref]

Yang, J.

X.-H. Bao, T.-Y. Chen, Q. Zhang, J. Yang, H. Zhang, T. Yang, and J.-W. Pan, “Optical nondestructive controlled-NOT gate without using entangled photons,” Phys. Rev. Lett. 98, 170502 (2007).
[Crossref]

Yang, L.

M. Asano, M. Bechu, M. Tame, Ş. K. Özdemir, R. Ikuta, D. Ö. Güney, T. Yamamoto, L. Yang, M. Wegener, and N. Imoto, “Distillation of photon entanglement using a plasmonic metamaterial,” Sci. Rep. 5, 18313 (2015).
[Crossref]

M. A. Al Farooqui, J. Breeland, M. I. Aslam, M. Sadatgol, Ş. K. Özdemir, M. Tame, L. Yang, and D. Ö. Güney, “Quantum entanglement distillation with metamaterials,” Opt. Express 23, 17941–17954 (2015).
[Crossref]

Yang, M.

K. Li, F.-Z. Kong, M. Yang, F. Ozaydin, Q. Yang, and Z.-L. Cao, “Generating multi-photon W-like states for perfect quantum teleportation and superdense coding,” Quantum Inf. Process. 15, 3137–3150 (2016).
[Crossref]

Yang, Q.

K. Li, F.-Z. Kong, M. Yang, F. Ozaydin, Q. Yang, and Z.-L. Cao, “Generating multi-photon W-like states for perfect quantum teleportation and superdense coding,” Quantum Inf. Process. 15, 3137–3150 (2016).
[Crossref]

Yang, T.

X.-H. Bao, T.-Y. Chen, Q. Zhang, J. Yang, H. Zhang, T. Yang, and J.-W. Pan, “Optical nondestructive controlled-NOT gate without using entangled photons,” Phys. Rev. Lett. 98, 170502 (2007).
[Crossref]

Z. Zhao, A.-N. Zhang, Y.-A. Chen, H. Zhang, J.-F. Du, T. Yang, and J.-W. Pan, “Experimental demonstration of a nondestructive controlled-not quantum gate for two independent photon qubits,” Phys. Rev. Lett. 94, 030501 (2005).
[Crossref]

Yang, X.

X. Yang, M.-Q. Bai, and Z.-W. Mo, “Controlled dense coding with the W state,” Int. J. Theor. Phys. 56, 3525–3533 (2017).
[Crossref]

Yuan, Z.-S.

Z.-S. Yuan, Y.-A. Chen, B. Zhao, S. Chen, J. Schmiedmayer, and J.-W. Pan, “Experimental demonstration of a BDCZ quantum repeater node,” Nature 454, 1098–1101 (2008).
[Crossref]

Zeilinger, A.

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
[Crossref]

S. Gasparoni, J.-W. Pan, P. Walther, T. Rudolph, and A. Zeilinger, “Realization of a photonic controlled-NOT gate sufficient for quantum computation,” Phys. Rev. Lett. 93, 020504 (2004).
[Crossref]

A. Zeilinger, “General properties of lossless beam splitters in interferometry,” Am. J. Phys. 49, 882–883 (1981).
[Crossref]

Zhang, A.-N.

Z. Zhao, A.-N. Zhang, Y.-A. Chen, H. Zhang, J.-F. Du, T. Yang, and J.-W. Pan, “Experimental demonstration of a nondestructive controlled-not quantum gate for two independent photon qubits,” Phys. Rev. Lett. 94, 030501 (2005).
[Crossref]

Zhang, H.

X.-H. Bao, T.-Y. Chen, Q. Zhang, J. Yang, H. Zhang, T. Yang, and J.-W. Pan, “Optical nondestructive controlled-NOT gate without using entangled photons,” Phys. Rev. Lett. 98, 170502 (2007).
[Crossref]

Z. Zhao, A.-N. Zhang, Y.-A. Chen, H. Zhang, J.-F. Du, T. Yang, and J.-W. Pan, “Experimental demonstration of a nondestructive controlled-not quantum gate for two independent photon qubits,” Phys. Rev. Lett. 94, 030501 (2005).
[Crossref]

Zhang, Q.

X.-H. Bao, T.-Y. Chen, Q. Zhang, J. Yang, H. Zhang, T. Yang, and J.-W. Pan, “Optical nondestructive controlled-NOT gate without using entangled photons,” Phys. Rev. Lett. 98, 170502 (2007).
[Crossref]

Zhang, X.

X. Zhang, J. E. Davis, and D. Ö. Güney, “Ultra-thin metamaterial beam splitters,” Appl. Sci. 10, 53 (2020).
[Crossref]

Zhao, B.

Z.-S. Yuan, Y.-A. Chen, B. Zhao, S. Chen, J. Schmiedmayer, and J.-W. Pan, “Experimental demonstration of a BDCZ quantum repeater node,” Nature 454, 1098–1101 (2008).
[Crossref]

Zhao, Z.

Z. Zhao, A.-N. Zhang, Y.-A. Chen, H. Zhang, J.-F. Du, T. Yang, and J.-W. Pan, “Experimental demonstration of a nondestructive controlled-not quantum gate for two independent photon qubits,” Phys. Rev. Lett. 94, 030501 (2005).
[Crossref]

Zhou, X.

X. Qiang, X. Zhou, J. Wang, C. M. Wilkes, T. Loke, S. O’Gara, L. Kling, G. D. Marshall, R. Santagati, T. C. Ralph, and J. B. Wang, “Large-scale silicon quantum photonics implementing arbitrary two-qubit processing,” Nat. Photonics 12, 534–539 (2018).
[Crossref]

Zhou, Y.-S.

Y.-S. Zhou, F. Wang, and M.-X. Luo, “Efficient superdense coding with W states,” Int. J. Theor. Phys. 57, 1935–1941 (2018).
[Crossref]

Zhu, S.

S. Wang, Q. Cheng, Y. Gong, P. Xu, C. Sun, L. Li, T. Li, and S. Zhu, “A 14×14 µm2 footprint polarization-encoded quantum controlled-NOT gate based on hybrid waveguide,” Nat. Commun. 7, 11490 (2016).
[Crossref]

Am. J. Phys. (1)

A. Zeilinger, “General properties of lossless beam splitters in interferometry,” Am. J. Phys. 49, 882–883 (1981).
[Crossref]

Appl. Sci. (1)

X. Zhang, J. E. Davis, and D. Ö. Güney, “Ultra-thin metamaterial beam splitters,” Appl. Sci. 10, 53 (2020).
[Crossref]

Commun. Theor. Phys. (3)

X. Xiao-Ming, D. Li, G. Ya-Jun, and C. Feng, “Quantum teleportation schemes of an N-particle state via three-particle general W states,” Commun. Theor. Phys. 49, 905 (2008).
[Crossref]

W. Jian, Z. Quan, and T. Chao-Jing, “Quantum secure communication scheme with W state,” Commun. Theor. Phys. 48, 637 (2007).
[Crossref]

D. Li, X. Xiao-Ming, G. Ya-Jun, and C. Feng, “Improvement on quantum secure direct communication with W state in noisy channel,” Commun. Theor. Phys. 51, 232 (2009).
[Crossref]

Int. J. Theor. Phys. (2)

Y.-S. Zhou, F. Wang, and M.-X. Luo, “Efficient superdense coding with W states,” Int. J. Theor. Phys. 57, 1935–1941 (2018).
[Crossref]

X. Yang, M.-Q. Bai, and Z.-W. Mo, “Controlled dense coding with the W state,” Int. J. Theor. Phys. 56, 3525–3533 (2017).
[Crossref]

J. Mod. Opt. (1)

J. Jeffers, “Interference and the lossless lossy beam splitter,” J. Mod. Opt. 47, 1819–1824 (2000).
[Crossref]

Nat. Commun. (1)

S. Wang, Q. Cheng, Y. Gong, P. Xu, C. Sun, L. Li, T. Li, and S. Zhu, “A 14×14 µm2 footprint polarization-encoded quantum controlled-NOT gate based on hybrid waveguide,” Nat. Commun. 7, 11490 (2016).
[Crossref]

Nat. Photonics (1)

X. Qiang, X. Zhou, J. Wang, C. M. Wilkes, T. Loke, S. O’Gara, L. Kling, G. D. Marshall, R. Santagati, T. C. Ralph, and J. B. Wang, “Large-scale silicon quantum photonics implementing arbitrary two-qubit processing,” Nat. Photonics 12, 534–539 (2018).
[Crossref]

Nat. Phys. (1)

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[Crossref]

Nature (4)

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
[Crossref]

Z.-S. Yuan, Y.-A. Chen, B. Zhao, S. Chen, J. Schmiedmayer, and J.-W. Pan, “Experimental demonstration of a BDCZ quantum repeater node,” Nature 454, 1098–1101 (2008).
[Crossref]

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, “Demonstration of an all-optical quantum controlled-NOT gate,” Nature 426, 264–267 (2003).
[Crossref]

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[Crossref]

New J. Phys. (1)

T. Tashima, Ş. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Local expansion of photonic W state using a polarization-dependent beamsplitter,” New J. Phys. 11, 023024 (2009).
[Crossref]

Opt. Commun. (1)

P. Tuong, J. Park, V. Lam, W. Jang, S. Nikitov, and Y. Lee, “Dielectric and Ohmic losses in perfectly absorbing metamaterials,” Opt. Commun. 295, 17–20 (2013).
[Crossref]

Opt. Express (2)

Opt. Spectrosc. (1)

P. Kok, “Creating large NOON states with imperfect phase control,” Opt. Spectrosc. 111, 520–522 (2011).
[Crossref]

Optica (1)

Phys. Lett. A (1)

B.-S. Shi and A. Tomita, “Teleportation of an unknown state by W state,” Phys. Lett. A 296, 161–164 (2002).
[Crossref]

Phys. Rev. A (10)

P. M. Alsing, E. E. Hach, C. C. Tison, and A. M. Smith, “Quantum-optical description of losses in ring resonators based on field-operator transformations,” Phys. Rev. A 95, 053828 (2017).
[Crossref]

S. M. Barnett, J. Jeffers, A. Gatti, and R. Loudon, “Quantum optics of lossy beam splitters,” Phys. Rev. A 57, 2134–2145 (1998).
[Crossref]

A. S. Clark, J. Fulconis, J. G. Rarity, W. J. Wadsworth, and J. L. O’Brien, “All-optical-fiber polarization-based quantum logic gate,” Phys. Rev. A 79, 030303 (2009).
[Crossref]

K. Sanaka, K. Kawahara, and T. Kuga, “Experimental probabilistic manipulation of down-converted photon pairs using unbalanced interferometers,” Phys. Rev. A 66, 040301 (2002).
[Crossref]

M. Koashi, T. Yamamoto, and N. Imoto, “Probabilistic manipulation of entangled photons,” Phys. Rev. A 63, 030301 (2001).
[Crossref]

T. Pittman, B. Jacobs, and J. Franson, “Probabilistic quantum logic operations using polarizing beam splitters,” Phys. Rev. A 64, 062311 (2001).
[Crossref]

T. Ralph, A. White, W. Munro, and G. Milburn, “Simple scheme for efficient linear optics quantum gates,” Phys. Rev. A 65, 012314 (2001).
[Crossref]

H. F. Hofmann and S. Takeuchi, “Quantum phase gate for photonic qubits using only beam splitters and postselection,” Phys. Rev. A 66, 024308 (2002).
[Crossref]

T. Pittman, M. Fitch, B. Jacobs, and J. Franson, “Experimental controlled-NOT logic gate for single photons in the coincidence basis,” Phys. Rev. A 68, 032316 (2003).
[Crossref]

T. C. Ralph, N. K. Langford, T. Bell, and A. White, “Linear optical controlled-NOT gate in the coincidence basis,” Phys. Rev. A 65, 062324 (2002).
[Crossref]

Phys. Rev. Lett. (12)

R. Okamoto, H. F. Hofmann, S. Takeuchi, and K. Sasaki, “Demonstration of an optical quantum controlled-NOT gate without path interference,” Phys. Rev. Lett. 95, 210506 (2005).
[Crossref]

J. Chen, J. B. Altepeter, M. Medic, K. F. Lee, B. Gokden, R. H. Hadfield, S. W. Nam, and P. Kumar, “Demonstration of a quantum controlled-NOT gate in the telecommunications band,” Phys. Rev. Lett. 100, 133603 (2008).
[Crossref]

N. K. Langford, T. Weinhold, R. Prevedel, K. Resch, A. Gilchrist, J. O’Brien, G. Pryde, and A. White, “Demonstration of a simple entangling optical gate and its use in Bell-state analysis,” Phys. Rev. Lett. 95, 210504 (2005).
[Crossref]

Z. Zhao, A.-N. Zhang, Y.-A. Chen, H. Zhang, J.-F. Du, T. Yang, and J.-W. Pan, “Experimental demonstration of a nondestructive controlled-not quantum gate for two independent photon qubits,” Phys. Rev. Lett. 94, 030501 (2005).
[Crossref]

N. Kiesel, C. Schmid, U. Weber, R. Ursin, and H. Weinfurter, “Linear optics controlled-phase gate made simple,” Phys. Rev. Lett. 95, 210505 (2005).
[Crossref]

M. A. Nielsen, “Optical quantum computation using cluster states,” Phys. Rev. Lett. 93, 040503 (2004).
[Crossref]

T. C. Ralph, A. Hayes, and A. Gilchrist, “Loss-tolerant optical qubits,” Phys. Rev. Lett. 95, 100501 (2005).
[Crossref]

T. Pittman, B. Jacobs, and J. Franson, “Demonstration of nondeterministic quantum logic operations using linear optical elements,” Phys. Rev. Lett. 88, 257902 (2002).
[Crossref]

B. P. Lanyon, T. J. Weinhold, N. K. Langford, M. Barbieri, D. F. James, A. Gilchrist, and A. G. White, “Experimental demonstration of a compiled version of Shor’s algorithm with quantum entanglement,” Phys. Rev. Lett. 99, 250505 (2007).
[Crossref]

J. L. O’Brien, G. Pryde, A. Gilchrist, D. James, N. K. Langford, T. Ralph, and A. White, “Quantum process tomography of a controlled-NOT gate,” Phys. Rev. Lett. 93, 080502 (2004).
[Crossref]

S. Gasparoni, J.-W. Pan, P. Walther, T. Rudolph, and A. Zeilinger, “Realization of a photonic controlled-NOT gate sufficient for quantum computation,” Phys. Rev. Lett. 93, 020504 (2004).
[Crossref]

X.-H. Bao, T.-Y. Chen, Q. Zhang, J. Yang, H. Zhang, T. Yang, and J.-W. Pan, “Optical nondestructive controlled-NOT gate without using entangled photons,” Phys. Rev. Lett. 98, 170502 (2007).
[Crossref]

Phys. Scripta (1)

H.-J. Cao and H.-S. Song, “Quantum secure direct communication scheme using a W state and teleportation,” Phys. Scripta 74, 572 (2006).
[Crossref]

Quantum Inf. Process. (2)

K. Li, F.-Z. Kong, M. Yang, F. Ozaydin, Q. Yang, and Z.-L. Cao, “Generating multi-photon W-like states for perfect quantum teleportation and superdense coding,” Quantum Inf. Process. 15, 3137–3150 (2016).
[Crossref]

A. Gueddana, P. Gholami, and V. Lakshminarayanan, “Can a universal quantum cloner be used to design an experimentally feasible near-deterministic CNOT gate?” Quantum Inf. Process. 18, 221 (2019).
[Crossref]

Rev. Mod. Phys. (1)

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135 (2007).
[Crossref]

Sci. Rep. (2)

M. Asano, M. Bechu, M. Tame, Ş. K. Özdemir, R. Ikuta, D. Ö. Güney, T. Yamamoto, L. Yang, M. Wegener, and N. Imoto, “Distillation of photon entanglement using a plasmonic metamaterial,” Sci. Rep. 5, 18313 (2015).
[Crossref]

A. Vora, J. Gwamuri, N. Pala, A. Kulkarni, J. M. Pearce, and D. Ö. Güney, “Exchanging Ohmic losses in metamaterial absorbers with useful optical absorption for photovoltaics,” Sci. Rep. 4, 4901 (2014).
[Crossref]

Science (1)

B. Vest, M.-C. Dheur, É. Devaux, A. Baron, E. Rousseau, J.-P. Hugonin, J.-J. Greffet, G. Messin, and F. Marquier, “Anti-coalescence of bosons on a lossy beam splitter,” Science 356, 1373–1376 (2017).
[Crossref]

Other (1)

M. A. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2010).

Supplementary Material (1)

NameDescription
Supplement 1       Phases of transmission and reflection coefficients.

Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

Cited By

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

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1. Schematic of a polarization-dependent beam splitter with the input and output operators indicated. The subscript $k$ represents polarization.
Fig. 2.
Fig. 2. Three-PDBS schematic for a LOQC CNOT gate. The dashed outline around the PDBSs signifies the controlled phase gate on which this design is based. The upper Hadamard gate prepares the input target qubit ${T_{{\rm in}}}$ for the CNOT operation [10] while the lower Hadamard gate converts the target qubit back into the H-V basis. ${T_{{\rm out}}}$ refers to the output target qubit. The first PDBS acquires the effective nonlinear sign shift while the other two are mainly for equalizing the probability amplitudes.
Fig. 3.
Fig. 3. Simplified schematic of the W-state expansion gate. Half-wave plate for the $\pi$ phase shift compensation is not shown.
Fig. 4.
Fig. 4. Schematic of a simplified CNOT structure utilizing a lossy PDBS where the PDBS has the properties given in Eq. (22).

Equations (37)

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

[ a ^ i , k ( ω ) , a ^ i , k ( ω ) ] = δ ( ω ω ) = [ b ^ i , k ( ω ) , b ^ i , k ( ω ) ] ,
[ a ^ i , k ( ω ) , b ^ i , k ( ω ) ] = 0 = [ b ^ i , k ( ω ) , a ^ i , k ( ω ) ] ,
[ a ^ i n , k ( ω ) , F ^ a , k ( ω ) ] = [ a ^ i n , k ( ω ) , F ^ b , k ( ω ) ] = [ a ^ i n , k ( ω ) , F ^ a , k ( ω ) ] = [ a ^ i n , k ( ω ) , F ^ b , k ( ω ) ] = 0 ,
[ F ^ a , k ( ω ) , F ^ a , k ( ω ) ] = δ ( ω ω ) { 1 | t ( ω ) | 2 | r ( ω ) | 2 } = [ F ^ b , k ( ω ) , F ^ b , k ( ω ) ] ,
[ F ^ a , k ( ω ) , F ^ b , k ( ω ) ] = δ ( ω ω ) { t ( ω ) r ( ω ) + t ( ω ) r ( ω ) } = [ F ^ b , k ( ω ) , F ^ a , k ( ω ) ] .
a ^ o u t , k ( ω ) = t a , k ( ω ) a ^ i n , k ( ω ) + r b , k ( ω ) b ^ i n , k ( ω ) + F ^ a , k ( ω ) ,
b ^ o u t , k ( ω ) = t b , k ( ω ) b ^ i n , k ( ω ) + r a , k ( ω ) a ^ i n , k ( ω ) + F ^ b , k ( ω ) ,
a ^ i n , k = 1 t a , k t b , k r a , k r b , k × ( t b , k a ^ o u t , k r b , k b ^ o u t , k t b , k F ^ a , k + r b , k F ^ b , k ) ,
b ^ i n , k = 1 t a , k t b , k r a , k r b , k ( t a , k b ^ o u t , k r a , k a ^ o u t , k t a , k F ^ b , k + r a , k F ^ a , k ) ,
| H H i n | H H o u t ,
| V V i n | V V o u t ,
| H V i n | H V o u t ,
| V H i n | V H o u t .
a ^ i n , k = j | t k | a ^ o u t , k + | r k | b ^ o u t , k ,
b ^ i n , k = j | t k | b ^ o u t , k + | r k | a ^ o u t , k ,
| H H i n | r H , 3 r H , 2 | ( | t H , 1 | 2 + | r H , 1 | 2 ) | H H o u t ,
| V V i n | r V , 3 r V , 2 | ( | t V , 1 | 2 + | r V , 1 | 2 ) | V V o u t ,
| H V i n | r H , 3 r V , 2 t H , 1 t V , 1 | | V H o u t + | r V , 3 r H , 2 r H , 1 r V , 1 | | H V o u t ,
| V H i n | r V , 3 r H , 2 t H , 1 t V , 1 | | H V o u t + | r H , 3 r V , 2 r H , 1 r V , 1 | | V H o u t ,
| H H i n α | H H o u t ,
| V V i n α | V V o u t ,
| H V i n 0 | V H o u t + α | H V o u t ,
| V H i n 0 | H V o u t + α | V H o u t ,
| t H , 1 | = | t V , 2 | = | t V , 3 | = 2 3 , | r H , 1 | = | r V , 2 | = | r V , 3 | = 1 3 , | t V , 1 | = | t H , 2 | = | t H , 3 | = 0 , | r V , 1 | = | r H , 2 | = | r H , 3 | = 1.
| ψ i n = ( | H 0 | V 1 + | V 0 | H 1 ) | H 2 .
| ψ o u t = ( | t 1 , H t 2 , H | + | r 1 , H r 2 , H | ) | V 0 | H 3 | H 4 + | r 2 , V r 1 , H | | H 0 | V 3 | H 4 | t 2 , V t 1 , H | | H 0 | H 3 | V 4 ,
| t 1 , H | = | t 2 , H | = | r 1 , V | = | r 2 , V | = 5 5 10 , | t 1 , V | = | t 2 , V | = | r 1 , H | = | r 2 , H | = 5 + 5 10 ,
| HH i n r H , 3 r H , 2 ( t H , 1 2 + r H , 1 2 ) ( t H , 3 2 r H , 3 2 ) ( t H , 2 2 r H , 2 2 ) ( t H , 1 2 r H , 1 2 ) 2 | HH o u t ,
| V V i n r V , 3 r V , 2 ( t V , 1 2 + r V , 1 2 ) ( t V , 3 2 r V , 3 2 ) ( t V , 2 2 r V , 2 2 ) ( t V , 1 2 r V , 1 2 ) 2 | V V o u t ,
| H V i n r H , 3 r V , 2 t V , 1 t H , 1 ( t H , 3 2 r H , 3 2 ) ( t V , 2 2 r V , 2 2 ) ( t V , 1 2 r V , 1 2 ) ( t H , 1 2 r H , 1 2 ) | V H o u t + r V , 3 r H , 2 r V , 1 r H , 1 ( t V , 3 2 r V , 3 2 ) ( t H , 2 2 r H , 2 2 ) ( t V , 1 2 r V , 1 2 ) ( t H , 1 2 r H , 1 2 ) | H V o u t ,
| V H i n r V , 3 r H , 2 t V , 1 t H , 1 ( t V , 3 2 r V , 3 2 ) ( t H , 2 2 r H , 2 2 ) ( t V , 1 2 r V , 1 2 ) ( t H , 1 2 r H , 1 2 ) | H V o u t + r H , 3 r V , 2 r V , 1 r H , 1 ( t H , 3 2 r H , 3 2 ) ( t V , 2 2 r V , 2 2 ) ( t V , 1 2 r V , 1 2 ) ( t H , 1 2 r H , 1 2 ) | V H o u t ,
| ψ o u t = t 1 , H t 2 , H + r 1 , H r 2 , H ( t 1 , H t 2 , H r 1 , H r 2 , H ) 2 | V 0 | H 3 | H 4 + r 2 , V r 1 , H | H 0 | V 3 | H 4 + t 2 , V t 1 , H | H 0 | H 3 | V 4 ( t 1 , V t 2 , V r 1 , V r 2 , V ) ( t 1 , H t 2 , H r 1 , H r 2 , H ) .
| H H i n ( | t H | 2 + | r H | 2 ) | H H o u t ,
| V V i n ( | t V | 2 + | r V | 2 ) | V V o u t ,
| H V i n | t H t V | | V H o u t + | r H r V | | H V o u t ,
| V H i n | t H t V | | H V o u t + | r H r V | | V H o u t ,
| t H | = 2 3 , | r H | = | r V | = 1 3 , | t V | = 0 ,

Metrics