Abstract

The direct counterfactual quantum communication (DCQC) is a surprising phenomenon that quantum information can be transmitted without using any carriers of physical particles. The nested interferometers are promising devices for realizing DCQC as long as the number of interferometers goes to be infinity. Considering the inevitable loss or dissipation in practical experimental interferometers, we analyze the dependence of reliability on the number of interferometers, and show that the reliability of direct communication is being rapidly degraded with the large number of interferometers. Furthermore, we simulate and test this counterfactual deterministic communication protocol with a finite number of interferometers, and demonstrate the improvement of the reliability using dissipation compensation in interferometers.

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

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    [Crossref] [PubMed]
  28. Z. Q. Yin, H. W. Li, W. Chen, Z. F. Han, and G. C. Guo, “Security of counterfactual quantum cryptography,” Phys. Rev. A 82(4), 042335 (2010).
    [Crossref]
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    [Crossref]
  32. G. S. Agarwal and S. P. Tewari, “An all-optical realization of the quantum Zeno effect,” Phys. Lett. A 185(2), 139–142 (1994).
    [Crossref]
  33. H. Salih, Z.-H. Li, M. Al-Amri, and M. S. Zubairy, “Protocol for direct counterfactual quantum communication,” Phys. Rev. Lett. 110(17), 170502 (2013).
    [Crossref] [PubMed]
  34. Y. Cao, Y. H. Li, Z. Cao, J. Yin, Y. A. Chen, H. L. Yin, T. Y. Chen, X. Ma, C. Z. Peng, and J. W. Pan, “Direct counterfactual communication via quantum Zeno effect,” Proc. Natl. Acad. Sci. U.S.A. 114(19), 4920–4924 (2017).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]

2017 (5)

S. K. Liao, W. Q. Cai, W. Y. Liu, L. Zhang, Y. Li, J. G. Ren, J. Yin, Q. Shen, Y. Cao, Z. P. Li, F. Z. Li, X. W. Chen, L. H. Sun, J. J. Jia, J. C. Wu, X. J. Jiang, J. F. Wang, Y. M. Huang, Q. Wang, Y. L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y. A. Chen, N. L. Liu, X. B. Wang, Z. C. Zhu, C. Y. Lu, R. Shu, C. Z. Peng, J. Y. Wang, and J. W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

W. Zhang, D. S. Ding, Y. B. Sheng, L. Zhou, B. S. Shi, and G. C. Guo, “Quantum secure direct communication with quantum memory,” Phys. Rev. Lett. 118(22), 220501 (2017).
[Crossref] [PubMed]

F. Zhu, W. Zhang, Y. B. Sheng, and Y. D. Huang, “Experimental long-distance quantum secure direct communication,” Science Bulletin 62(22), 1519–1524 (2017).
[Crossref]

Y. Cao, Y. H. Li, Z. Cao, J. Yin, Y. A. Chen, H. L. Yin, T. Y. Chen, X. Ma, C. Z. Peng, and J. W. Pan, “Direct counterfactual communication via quantum Zeno effect,” Proc. Natl. Acad. Sci. U.S.A. 114(19), 4920–4924 (2017).
[Crossref] [PubMed]

C. Liu, J. Liu, J. Zhang, and S. Zhu, “The experimental demonstration of high efficiency interaction-free measurement for quantum counterfactual-like communication,” Sci. Rep. 7(1), 10875 (2017).
[Crossref] [PubMed]

2016 (1)

J. Y. Hu, B. Yu, M. Y. Jing, L. T. Xiao, S. T. Jia, G. Q. Qin, and G. L. Long, “Experimental quantum secure direct communication with single photons,” Light Sci. Appl. 5(9), e16144 (2016).
[Crossref]

2015 (1)

J. Peise, B. Lücke, L. Pezzé, F. Deuretzbacher, W. Ertmer, J. Arlt, A. Smerzi, L. Santos, and C. Klempt, “Interaction-free measurements by quantum Zeno stabilization of ultracold atoms,” Nat. Commun. 6, 6811 (2015).
[Crossref] [PubMed]

2013 (2)

A. Danan, D. Farfurnik, S. Bar-Ad, and L. Vaidman, “Asking photons where they have been,” Phys. Rev. Lett. 111(24), 240402 (2013).
[Crossref] [PubMed]

H. Salih, Z.-H. Li, M. Al-Amri, and M. S. Zubairy, “Protocol for direct counterfactual quantum communication,” Phys. Rev. Lett. 110(17), 170502 (2013).
[Crossref] [PubMed]

2012 (2)

G. Brida, A. Cavanna, I. P. Degiovanni, M. Genovese, and P. Traina, “Experimental realization of counterfactual quantum cryptography,” Laser Phys. Lett. 9(3), 247–252 (2012).
[Crossref]

Y. Liu, L. Ju, X. L. Liang, S. B. Tang, G. L. Tu, L. Zhou, C. Z. Peng, K. Chen, T. Y. Chen, Z. B. Chen, and J. W. Pan, “Experimental demonstration of counterfactual quantum communication,” Phys. Rev. Lett. 109(3), 030501 (2012).
[Crossref] [PubMed]

2010 (1)

Z. Q. Yin, H. W. Li, W. Chen, Z. F. Han, and G. C. Guo, “Security of counterfactual quantum cryptography,” Phys. Rev. A 82(4), 042335 (2010).
[Crossref]

2009 (3)

T. G. Noh, “Counterfactual quantum cryptography,” Phys. Rev. Lett. 103(23), 230501 (2009).
[Crossref] [PubMed]

R. García-Patrón and N. J. Cerf, “Continuous-variable quantum key distribution protocols over noisy channels,” Phys. Rev. Lett. 102(13), 130501 (2009).
[Crossref] [PubMed]

X. B. Wang, L. Yang, C. Z. Peng, and J. W. Pan, “Decoy-state quantum key distribution with both source errors and statistical fluctuations,” New J. Phys. 11(7), 075006 (2009).
[Crossref]

2008 (1)

L. Xiao, C. Wang, W. Zhang, Y. D. Huang, J. D. Peng, and G. L. Long, “Efficient strategy for sharing entanglement via noisy channels with doubly entangled photon pairs,” Phys. Rev. A 77(4), 042315 (2008).
[Crossref]

2005 (1)

X. B. Wang, “Beating the photon-number-splitting attack in practical quantum cryptography,” Phys. Rev. Lett. 94(23), 230503 (2005).
[Crossref] [PubMed]

2004 (2)

F. G. Deng and G. L. Long, “Secure direct communication with a quantum one-time pad,” Phys. Rev. A 69(5), 052319 (2004).
[Crossref]

V. Scarani, A. Acín, G. Ribordy, and N. Gisin, “Quantum cryptography protocols robust against photon number splitting attacks for weak laser pulse implementations,” Phys. Rev. Lett. 92(5), 057901 (2004).
[Crossref] [PubMed]

2003 (1)

F. G. Deng, G. L. Long, and X. S. Liu, “Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block,” Phys. Rev. A 68(4), 042317 (2003).
[Crossref]

2002 (2)

G. L. Long and X. S. Liu, “Theoretically efficient high-capacity quantum-key-distribution scheme,” Phys. Rev. A 65(3), 032302 (2002).
[Crossref]

C. Silberhorn, N. Korolkova, and G. Leuchs, “Quantum key distribution with bright entangled beams,” Phys. Rev. Lett. 88(16), 167902 (2002).
[Crossref] [PubMed]

2001 (3)

W. Y. Hwang, D. Ahn, and S. W. Hwang, “Quantum gambling using two nonorthogonal states,” Phys. Rev. A 64(6), 064302 (2001).
[Crossref]

L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
[Crossref] [PubMed]

N. J. Cerf, M. Lévy, and G. V. Assche, “Quantum distribution of Gaussian keys using squeezed states,” Phys. Rev. A 63(5), 052311 (2001).
[Crossref]

1999 (3)

G. C. Guo and B. S. Shi, “Quantum cryptography based on interaction-free measurement,” Phys. Lett. A 256(2-3), 109–112 (1999).
[Crossref]

H. K. Lo and H. F. Chau, “Unconditional security of quantum key distribution over arbitrarily long distances,” Science 283(5410), 2050–2056 (1999).
[Crossref] [PubMed]

P. G. Kwiat, A. G. White, J. R. Mitchell, O. Nairz, G. Weihs, H. Weinfurter, and A. Zeilinger, “High-efficiency quantum interrogation measurements via the quantum zeno effect,” Phys. Rev. Lett. 83(23), 4725–4728 (1999).
[Crossref]

1995 (1)

B. Huttner, N. Imoto, N. Gisin, and T. Mor, “Quantum cryptography with coherent states,” Phys. Rev. A 51(3), 1863–1869 (1995).
[Crossref] [PubMed]

1994 (1)

G. S. Agarwal and S. P. Tewari, “An all-optical realization of the quantum Zeno effect,” Phys. Lett. A 185(2), 139–142 (1994).
[Crossref]

1993 (1)

A. C. Elitzur and L. Vaidman, “Quantum mechanical interaction-free measurements,” Found. Phys. 23(7), 987–997 (1993).
[Crossref]

1992 (2)

C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without bell’s theorem,” Phys. Rev. Lett. 68(5), 557–559 (1992).
[Crossref] [PubMed]

C. H. Bennett, “Quantum cryptography using any two nonorthogonal states,” Phys. Rev. Lett. 68(21), 3121–3124 (1992).
[Crossref] [PubMed]

1991 (1)

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67(6), 661–663 (1991).
[Crossref] [PubMed]

1980 (1)

A. Peres, “Zeno paradox in quantum theory,” Am. J. Phys. 48(11), 931–932 (1980).
[Crossref]

1977 (1)

B. Misra and E. C. G. Sudarshan, “The Zeno’s paradox in quantum theory,” Phys. 18(4), 756–763 (1977).
[Crossref]

Acín, A.

V. Scarani, A. Acín, G. Ribordy, and N. Gisin, “Quantum cryptography protocols robust against photon number splitting attacks for weak laser pulse implementations,” Phys. Rev. Lett. 92(5), 057901 (2004).
[Crossref] [PubMed]

Agarwal, G. S.

G. S. Agarwal and S. P. Tewari, “An all-optical realization of the quantum Zeno effect,” Phys. Lett. A 185(2), 139–142 (1994).
[Crossref]

Ahn, D.

W. Y. Hwang, D. Ahn, and S. W. Hwang, “Quantum gambling using two nonorthogonal states,” Phys. Rev. A 64(6), 064302 (2001).
[Crossref]

Al-Amri, M.

H. Salih, Z.-H. Li, M. Al-Amri, and M. S. Zubairy, “Protocol for direct counterfactual quantum communication,” Phys. Rev. Lett. 110(17), 170502 (2013).
[Crossref] [PubMed]

Arlt, J.

J. Peise, B. Lücke, L. Pezzé, F. Deuretzbacher, W. Ertmer, J. Arlt, A. Smerzi, L. Santos, and C. Klempt, “Interaction-free measurements by quantum Zeno stabilization of ultracold atoms,” Nat. Commun. 6, 6811 (2015).
[Crossref] [PubMed]

Assche, G. V.

N. J. Cerf, M. Lévy, and G. V. Assche, “Quantum distribution of Gaussian keys using squeezed states,” Phys. Rev. A 63(5), 052311 (2001).
[Crossref]

Bar-Ad, S.

A. Danan, D. Farfurnik, S. Bar-Ad, and L. Vaidman, “Asking photons where they have been,” Phys. Rev. Lett. 111(24), 240402 (2013).
[Crossref] [PubMed]

Bennett, C. H.

C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without bell’s theorem,” Phys. Rev. Lett. 68(5), 557–559 (1992).
[Crossref] [PubMed]

C. H. Bennett, “Quantum cryptography using any two nonorthogonal states,” Phys. Rev. Lett. 68(21), 3121–3124 (1992).
[Crossref] [PubMed]

Brassard, G.

C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without bell’s theorem,” Phys. Rev. Lett. 68(5), 557–559 (1992).
[Crossref] [PubMed]

Brida, G.

G. Brida, A. Cavanna, I. P. Degiovanni, M. Genovese, and P. Traina, “Experimental realization of counterfactual quantum cryptography,” Laser Phys. Lett. 9(3), 247–252 (2012).
[Crossref]

Cai, W. Q.

S. K. Liao, W. Q. Cai, W. Y. Liu, L. Zhang, Y. Li, J. G. Ren, J. Yin, Q. Shen, Y. Cao, Z. P. Li, F. Z. Li, X. W. Chen, L. H. Sun, J. J. Jia, J. C. Wu, X. J. Jiang, J. F. Wang, Y. M. Huang, Q. Wang, Y. L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y. A. Chen, N. L. Liu, X. B. Wang, Z. C. Zhu, C. Y. Lu, R. Shu, C. Z. Peng, J. Y. Wang, and J. W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Cao, Y.

S. K. Liao, W. Q. Cai, W. Y. Liu, L. Zhang, Y. Li, J. G. Ren, J. Yin, Q. Shen, Y. Cao, Z. P. Li, F. Z. Li, X. W. Chen, L. H. Sun, J. J. Jia, J. C. Wu, X. J. Jiang, J. F. Wang, Y. M. Huang, Q. Wang, Y. L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y. A. Chen, N. L. Liu, X. B. Wang, Z. C. Zhu, C. Y. Lu, R. Shu, C. Z. Peng, J. Y. Wang, and J. W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Y. Cao, Y. H. Li, Z. Cao, J. Yin, Y. A. Chen, H. L. Yin, T. Y. Chen, X. Ma, C. Z. Peng, and J. W. Pan, “Direct counterfactual communication via quantum Zeno effect,” Proc. Natl. Acad. Sci. U.S.A. 114(19), 4920–4924 (2017).
[Crossref] [PubMed]

Cao, Z.

Y. Cao, Y. H. Li, Z. Cao, J. Yin, Y. A. Chen, H. L. Yin, T. Y. Chen, X. Ma, C. Z. Peng, and J. W. Pan, “Direct counterfactual communication via quantum Zeno effect,” Proc. Natl. Acad. Sci. U.S.A. 114(19), 4920–4924 (2017).
[Crossref] [PubMed]

Cavanna, A.

G. Brida, A. Cavanna, I. P. Degiovanni, M. Genovese, and P. Traina, “Experimental realization of counterfactual quantum cryptography,” Laser Phys. Lett. 9(3), 247–252 (2012).
[Crossref]

Cerf, N. J.

R. García-Patrón and N. J. Cerf, “Continuous-variable quantum key distribution protocols over noisy channels,” Phys. Rev. Lett. 102(13), 130501 (2009).
[Crossref] [PubMed]

N. J. Cerf, M. Lévy, and G. V. Assche, “Quantum distribution of Gaussian keys using squeezed states,” Phys. Rev. A 63(5), 052311 (2001).
[Crossref]

Chau, H. F.

H. K. Lo and H. F. Chau, “Unconditional security of quantum key distribution over arbitrarily long distances,” Science 283(5410), 2050–2056 (1999).
[Crossref] [PubMed]

Chen, K.

Y. Liu, L. Ju, X. L. Liang, S. B. Tang, G. L. Tu, L. Zhou, C. Z. Peng, K. Chen, T. Y. Chen, Z. B. Chen, and J. W. Pan, “Experimental demonstration of counterfactual quantum communication,” Phys. Rev. Lett. 109(3), 030501 (2012).
[Crossref] [PubMed]

Chen, T. Y.

Y. Cao, Y. H. Li, Z. Cao, J. Yin, Y. A. Chen, H. L. Yin, T. Y. Chen, X. Ma, C. Z. Peng, and J. W. Pan, “Direct counterfactual communication via quantum Zeno effect,” Proc. Natl. Acad. Sci. U.S.A. 114(19), 4920–4924 (2017).
[Crossref] [PubMed]

Y. Liu, L. Ju, X. L. Liang, S. B. Tang, G. L. Tu, L. Zhou, C. Z. Peng, K. Chen, T. Y. Chen, Z. B. Chen, and J. W. Pan, “Experimental demonstration of counterfactual quantum communication,” Phys. Rev. Lett. 109(3), 030501 (2012).
[Crossref] [PubMed]

Chen, W.

Z. Q. Yin, H. W. Li, W. Chen, Z. F. Han, and G. C. Guo, “Security of counterfactual quantum cryptography,” Phys. Rev. A 82(4), 042335 (2010).
[Crossref]

Chen, X. W.

S. K. Liao, W. Q. Cai, W. Y. Liu, L. Zhang, Y. Li, J. G. Ren, J. Yin, Q. Shen, Y. Cao, Z. P. Li, F. Z. Li, X. W. Chen, L. H. Sun, J. J. Jia, J. C. Wu, X. J. Jiang, J. F. Wang, Y. M. Huang, Q. Wang, Y. L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y. A. Chen, N. L. Liu, X. B. Wang, Z. C. Zhu, C. Y. Lu, R. Shu, C. Z. Peng, J. Y. Wang, and J. W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Chen, Y. A.

S. K. Liao, W. Q. Cai, W. Y. Liu, L. Zhang, Y. Li, J. G. Ren, J. Yin, Q. Shen, Y. Cao, Z. P. Li, F. Z. Li, X. W. Chen, L. H. Sun, J. J. Jia, J. C. Wu, X. J. Jiang, J. F. Wang, Y. M. Huang, Q. Wang, Y. L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y. A. Chen, N. L. Liu, X. B. Wang, Z. C. Zhu, C. Y. Lu, R. Shu, C. Z. Peng, J. Y. Wang, and J. W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Y. Cao, Y. H. Li, Z. Cao, J. Yin, Y. A. Chen, H. L. Yin, T. Y. Chen, X. Ma, C. Z. Peng, and J. W. Pan, “Direct counterfactual communication via quantum Zeno effect,” Proc. Natl. Acad. Sci. U.S.A. 114(19), 4920–4924 (2017).
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Chen, Z. B.

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram of the nested interferometers for direct communication.

Fig. 2
Fig. 2

The output probability without loss or dissipation: (a) P(D1) at D1. (b) P(D2) at D2; The output probability with loss or dissipation: (c) P(D1) at D1. (d) P(D2) at D2.

Fig. 3
Fig. 3

The output probability with loss or dissipation for finite M and N. (a) and (b) P(D1) at D1 and P(D2) at D2 for logic 0; (c) and (d) P(D1) at D1 and P(D2) at D2 for logic 1.

Fig. 4
Fig. 4

The reliability as function of the dissipation δ 1 ( δ 2 =0.9 δ 1 , δ 3 =0.9 δ 2 ) for (a) logic 0 and (b) logic 1 with M = 3, N = 8.

Fig. 5
Fig. 5

The optimized experimental system of the direct communication

Fig. 6
Fig. 6

The improved reliability η 0 vs balanced dissipation δ c

Equations (10)

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Γ Μ =( 1 δ 1 0 0 1 δ 2 Ν ), Γ N =( 1 δ 2 0 0 1 δ 3 Ν ).
W M =( e iφ 0 0 1 ), W N =( 1 0 0 e iφ ),
T B S M =( r m t m t m r m ), T B S N ( r n t n t n r n ),
T w(0) = ( T B S M T M W M Γ M ) M1 T B S M ,
T M ( 1 0 0 cos N π 2N ).
T w(1) = ( T B S M W M Γ D ) M1 T B S M .
Γ D =( 1 δ 1 0 0 T 11 inn ),
T inn = ( T B S N W N Γ N ) N1 T B S N .
T C w(0) = ( T B S M T M W M Γ C ) M1 T B S M ,
Γ C =( 1( δ 1 + δ c ) 0 0 (1 δ 2 ) N ),