Abstract

We propose an alternative entanglement swapping scheme based on the principle of the counterfactual quantum communication, which demonstrates nonlocal entanglement swapping can be achieved by the operations of a third party. During the whole process, it is not needed to transmit any physical particles among the participants. Furthermore, all the entangled particles are not destroyed in the counterfactual entanglement swapping process, which means we can obtain two pairs of nonlocal entanglement at the same time, thus achieve high-efficiency entanglement distribution. The numerical analysis about the performance of the presented scheme shows that this counterfactual protocol can be implemented with high success probability and fidelity in the ideal asymptotic limit. The scheme may be meaningful for large-scale quantum communication network and quantum repeater.

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

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  41. X.-s. Ma, S. Zotter, J. Kofler, R. Ursin, T. Jennewein, C. Brukner, and A. Zeilinger, “Experimental delayed-choice entanglement swapping,” Nat. Phys. 8, 479–484 (2012).
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    [Crossref] [PubMed]
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2018 (1)

2017 (3)

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. USA 114, 4920 (2017).
[Crossref] [PubMed]

Q. Guo, S. Zhai, L.-Y. Cheng, H.-F. Wang, and S. Zhang, “Counterfactual quantum cloning without transmitting any physical particles,” Phys. Rev. A 96, 052335 (2017).
[Crossref]

D. R. M. Arvidsson-Shukur, A. N. O. Gottfries, and C. H. W. Barnes, “Evaluation of counterfactuality in counterfactual communication protocols,” Phys. Rev. A 96, 062316 (2017).
[Crossref]

2016 (2)

D. R. M. Arvidsson-Shukur and C. H. W. Barnes, “Quantum counterfactual communication without a weak trace,” Phys. Rev. A 94, 062303 (2016).
[Crossref]

L. Vaidman, “Comment on ‘Direct counterfactual transmission of a quantum state’,” Phys. Rev. A 93, 066301 (2016).
[Crossref]

2015 (6)

Y. Chen, X. Gu, D. Jiang, L. Xie, and L. Chen, “Tripartite counterfactual entanglement distribution,” Opt. Express 23, 21193–21203 (2015).
[Crossref] [PubMed]

L. Vaidman, “Counterfactuality of ‘counterfactual’ communication,” J. Phys. A: Math. Theor. 48, 465303 (2015).
[Crossref]

F. Kong, C. Ju, P. Huang, P. Wang, X. Kong, F. Shi, L. Jiang, and J. Du, “Experimental realization of high-efficiency counterfactual computation,” Phys. Rev. Lett. 115, 080501 (2015).
[Crossref] [PubMed]

A. Shenoy-Hejamadi and R. Srikanth, “Counterfactual distribution of Schrödinger cat states,” Phys. Rev. A 92, 062308 (2015).
[Crossref]

Q. Guo, L. Y. Cheng, L. Chen, H. F. Wang, and S. Zhang, “Counterfactual quantum-information transfer without transmitting any physical particles,” Sci. Rep. 5, 8416 (2015).
[Crossref] [PubMed]

Z. H. Li, M. Al-Amri, and M. S. Zubairy, “Direct counterfactual transmission of a quantum state,” Phys. Rev. A 92, 052315 (2015).
[Crossref]

2014 (5)

Z. H. Li, M. Al-Amri, and M. S. Zubairy, “Direct quantum communication with almost invisible photons,” Phys. Rev. A 89, 052334 (2014).
[Crossref]

Q. Guo, L. Y. Cheng, L. Chen, H. F. Wang, and S. Zhang, “Counterfactual entanglement distribution without transmitting any particles,” Opt. Express 22, 8970–8984 (2014).
[Crossref] [PubMed]

L. Vaidman, “Comment on ‘Protocol for direct counterfactual quantum communication’,” Phys. Rev. Lett. 112, 208901 (2014).
[Crossref]

H. Salih, Z. H. Li, M. Al-Amri, and M. S. Zubairy, “Salih et al. Reply,” Phys. Rev. Lett. 112, 208902 (2014).
[Crossref]

A. Reiserer, N. Kalb, G. Rempe, and S. Ritter, “A quantum gate between a flying optical photon and a single trapped atom,” Nature (London) 508, 237–240 (2014).
[Crossref]

2013 (6)

A. Reiserer, S. Ritter, and G. Rempe, “Nondestructive detection of an optical photon,” Science 342, 1349 (2013).
[Crossref] [PubMed]

C. Junge, D. O’Shea, J. Volz, and A. Rauschenbeutel, “Strong coupling between single atoms and nontransversal photons,” Phys. Rev. Lett. 110, 213604 (2013).
[Crossref] [PubMed]

E. Megidish, A. Halevy, T. Shacham, T. Dvir, L. Dovrat, and H. S. Eisenberg, “Entanglement swapping between photons that have never coexisted,” Phys. Rev. Lett. 110, 210403 (2013).
[Crossref] [PubMed]

N. Gisin, “Optical communication without photons,” Phys. Rev. A 88, 030301 (2013).
[Crossref]

J. L. Zhang, F. Z. Guo, F. Gao, B. Liu, and Q. Y. Wen, “Private database queries based on counterfactual quantum key distribution,” Phys. Rev. A 88, 022334 (2013).
[Crossref]

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

2012 (5)

Y. Liu, L. Ju, X. L. Liang, S. B. Tang, G. L. Shen 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, 030501 (2012).
[Crossref] [PubMed]

Z. Q. Yin, H. W. Li, Y. Yao, C. M. Zhang, S. Wang, W. Chen, G. C. Guo, and Z. F. Han, “Counterfactual quantum cryptography based on weak coherent states,” Phy. Rev. A 86, 022313 (2012).
[Crossref]

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

X.-s. Ma, S. Zotter, J. Kofler, R. Ursin, T. Jennewein, C. Brukner, and A. Zeilinger, “Experimental delayed-choice entanglement swapping,” Nat. Phys. 8, 479–484 (2012).
[Crossref]

E. Megidish, T. Shacham, A. Halevy, L. Dovrat, and H. S. Eisenberg, “Resource efficient source of multiphoton polarization entanglement,” Phys. Rev. Lett. 109, 080504 (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,” Phy. Rev. A 82, 042335 (2010).
[Crossref]

2009 (1)

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

2008 (1)

A. M. Goebel, C. Wagenknecht, Q. Zhang, Y.-A. Chen, K. Chen, J. Schmiedmayer, and J.-W. Pan, “Multistage entanglement swapping,” Phys. Rev. Lett. 101, 080403 (2008).
[Crossref] [PubMed]

2007 (2)

L. Vaidman, “Impossibility of the counterfactual computation for all possible outcomes,” Phys. Rev. Lett. 98, 160403 (2007).
[Crossref] [PubMed]

P. Kok, W. J. Munro, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[Crossref]

2006 (2)

D. D. Yavuz, P. B. Kulatunga, E. Urban, T. A. Johnson, N. Proite, T. Henage, T. G. Walker, and M. Saffman, “Fast ground state manipulation of neutral atoms in microscopic optical traps,” Phys. Rev. Lett. 96, 063001 (2006).
[Crossref] [PubMed]

O. Hosten, M. T. Rakher, J. T. Barreiro, N. A. Peters, and P. G. Kwiat, “Counterfactual quantum computation through quantum interrogation,” Nature (London) 439, 949–952 (2006).
[Crossref]

2005 (1)

J. Cho and H.-W. Lee, “Generation of atomic cluster states through the cavity input-output process,” Phys. Rev. Lett. 95, 160501 (2005).
[Crossref] [PubMed]

2004 (3)

L.-M. Duan and H. J. Kimble, “Scalable photonic quantum computation through cavity-assisted interactions,” Phys. Rev. Lett. 92, 127902 (2004).
[Crossref] [PubMed]

A. Boca, R. Miller, K. M. Birnbaum, A. D. Boozer, J. McKeever, and H. J. Kimble, “Observation of the vacuum rabi spectrum for one trapped atom,” Phys. Rev. Lett. 93, 233603 (2004).
[Crossref] [PubMed]

K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-not gate,” Phys. Rev. Lett. 93, 250502 (2004).
[Crossref]

2001 (1)

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

2000 (1)

A. Peres, “Delayed choice for entanglement swapping,” J. Mod. Opt. 47, 139–143 (2000).
[Crossref]

1999 (1)

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, 4725–4728 (1999).
[Crossref]

1998 (3)

S. Bose, V. Vedral, and P. L. Knight, “Multiparticle generalization of entanglement swapping,” Phys. Rev. A 57, 822–829 (1998).
[Crossref]

J.-W. Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental entanglement swapping: entangling photons that never interacted,” Phys. Rev. Lett. 80, 3891–3894 (1998).
[Crossref]

H.-J. Briegel, W. Dür, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81, 5932 (1998).
[Crossref]

1995 (1)

P. Kwiat, H. Weinfurter, T. Herzog, A. Zeilinger, and M. A. Kasevich, “Interaction-free measurement,” Phys. Rev. Lett. 74, 4763–4766 (1995).
[Crossref] [PubMed]

1993 (2)

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

M. Zukowski, A. Zeilinger, M. A. Horne, and A. Ekert, “‘Event-Ready-Detectors’ Bell experiment via entanglement swapping,” Phys. Rev. Lett. 71, 4287–4290 (1993).
[Crossref] [PubMed]

Aharonov, Y.

Y. Aharonov and L. Vaidman, “Modification of ‘Counterfactual communication protocols’ which makes them truly counterfactual,” arXiv:1805.10634 (2018).

Al-Amri, M.

Z. H. Li, M. Al-Amri, and M. S. Zubairy, “Direct counterfactual transmission of a quantum state,” Phys. Rev. A 92, 052315 (2015).
[Crossref]

Z. H. Li, M. Al-Amri, and M. S. Zubairy, “Direct quantum communication with almost invisible photons,” Phys. Rev. A 89, 052334 (2014).
[Crossref]

H. Salih, Z. H. Li, M. Al-Amri, and M. S. Zubairy, “Salih et al. Reply,” Phys. Rev. Lett. 112, 208902 (2014).
[Crossref]

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

Arvidsson-Shukur, D. R. M.

D. R. M. Arvidsson-Shukur, A. N. O. Gottfries, and C. H. W. Barnes, “Evaluation of counterfactuality in counterfactual communication protocols,” Phys. Rev. A 96, 062316 (2017).
[Crossref]

D. R. M. Arvidsson-Shukur and C. H. W. Barnes, “Quantum counterfactual communication without a weak trace,” Phys. Rev. A 94, 062303 (2016).
[Crossref]

Barnes, C. H. W.

D. R. M. Arvidsson-Shukur, A. N. O. Gottfries, and C. H. W. Barnes, “Evaluation of counterfactuality in counterfactual communication protocols,” Phys. Rev. A 96, 062316 (2017).
[Crossref]

D. R. M. Arvidsson-Shukur and C. H. W. Barnes, “Quantum counterfactual communication without a weak trace,” Phys. Rev. A 94, 062303 (2016).
[Crossref]

Barreiro, J. T.

O. Hosten, M. T. Rakher, J. T. Barreiro, N. A. Peters, and P. G. Kwiat, “Counterfactual quantum computation through quantum interrogation,” Nature (London) 439, 949–952 (2006).
[Crossref]

Birnbaum, K. M.

A. Boca, R. Miller, K. M. Birnbaum, A. D. Boozer, J. McKeever, and H. J. Kimble, “Observation of the vacuum rabi spectrum for one trapped atom,” Phys. Rev. Lett. 93, 233603 (2004).
[Crossref] [PubMed]

Boca, A.

A. Boca, R. Miller, K. M. Birnbaum, A. D. Boozer, J. McKeever, and H. J. Kimble, “Observation of the vacuum rabi spectrum for one trapped atom,” Phys. Rev. Lett. 93, 233603 (2004).
[Crossref] [PubMed]

Boozer, A. D.

A. Boca, R. Miller, K. M. Birnbaum, A. D. Boozer, J. McKeever, and H. J. Kimble, “Observation of the vacuum rabi spectrum for one trapped atom,” Phys. Rev. Lett. 93, 233603 (2004).
[Crossref] [PubMed]

Bose, S.

S. Bose, V. Vedral, and P. L. Knight, “Multiparticle generalization of entanglement swapping,” Phys. Rev. A 57, 822–829 (1998).
[Crossref]

Bouwmeester, D.

J.-W. Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental entanglement swapping: entangling photons that never interacted,” Phys. Rev. Lett. 80, 3891–3894 (1998).
[Crossref]

Brida, G.

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

Briegel, H.-J.

H.-J. Briegel, W. Dür, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81, 5932 (1998).
[Crossref]

Brukner, C.

X.-s. Ma, S. Zotter, J. Kofler, R. Ursin, T. Jennewein, C. Brukner, and A. Zeilinger, “Experimental delayed-choice entanglement swapping,” Nat. Phys. 8, 479–484 (2012).
[Crossref]

Cao, 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. USA 114, 4920 (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. USA 114, 4920 (2017).
[Crossref] [PubMed]

Cavanna, A.

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O. Hosten, M. T. Rakher, J. T. Barreiro, N. A. Peters, and P. G. Kwiat, “Counterfactual quantum computation through quantum interrogation,” Nature (London) 439, 949–952 (2006).
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Ralph, T. C.

P. Kok, W. J. Munro, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
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Rarity, J.

H. Salih, W. McCutcheon, and J. Rarity, “Do the laws of physics prohibit counterfactual communication?” arXiv:1806.01257 (2018).

Rauschenbeutel, A.

C. Junge, D. O’Shea, J. Volz, and A. Rauschenbeutel, “Strong coupling between single atoms and nontransversal photons,” Phys. Rev. Lett. 110, 213604 (2013).
[Crossref] [PubMed]

Reiserer, A.

A. Reiserer, N. Kalb, G. Rempe, and S. Ritter, “A quantum gate between a flying optical photon and a single trapped atom,” Nature (London) 508, 237–240 (2014).
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A. Reiserer, S. Ritter, and G. Rempe, “Nondestructive detection of an optical photon,” Science 342, 1349 (2013).
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Rempe, G.

A. Reiserer, N. Kalb, G. Rempe, and S. Ritter, “A quantum gate between a flying optical photon and a single trapped atom,” Nature (London) 508, 237–240 (2014).
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A. Reiserer, S. Ritter, and G. Rempe, “Nondestructive detection of an optical photon,” Science 342, 1349 (2013).
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Ritter, S.

A. Reiserer, N. Kalb, G. Rempe, and S. Ritter, “A quantum gate between a flying optical photon and a single trapped atom,” Nature (London) 508, 237–240 (2014).
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A. Reiserer, S. Ritter, and G. Rempe, “Nondestructive detection of an optical photon,” Science 342, 1349 (2013).
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Saffman, M.

D. D. Yavuz, P. B. Kulatunga, E. Urban, T. A. Johnson, N. Proite, T. Henage, T. G. Walker, and M. Saffman, “Fast ground state manipulation of neutral atoms in microscopic optical traps,” Phys. Rev. Lett. 96, 063001 (2006).
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Salih, H.

H. Salih, Z. H. Li, M. Al-Amri, and M. S. Zubairy, “Salih et al. Reply,” Phys. Rev. Lett. 112, 208902 (2014).
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H. Salih, Z. H. Li, M. Al-Amri, and M. S. Zubairy, “Protocol for direct counterfactual quantum communication,” Phys. Rev. Lett. 110, 170502 (2013).
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H. Salih, “From a quantum paradox to provably counterfactual disembodied transport: counterportation,” arXiv:1807.06586 (2018).

H. Salih, W. McCutcheon, and J. Rarity, “Do the laws of physics prohibit counterfactual communication?” arXiv:1806.01257 (2018).

Schmiedmayer, J.

A. M. Goebel, C. Wagenknecht, Q. Zhang, Y.-A. Chen, K. Chen, J. Schmiedmayer, and J.-W. Pan, “Multistage entanglement swapping,” Phys. Rev. Lett. 101, 080403 (2008).
[Crossref] [PubMed]

Shacham, T.

E. Megidish, A. Halevy, T. Shacham, T. Dvir, L. Dovrat, and H. S. Eisenberg, “Entanglement swapping between photons that have never coexisted,” Phys. Rev. Lett. 110, 210403 (2013).
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E. Megidish, T. Shacham, A. Halevy, L. Dovrat, and H. S. Eisenberg, “Resource efficient source of multiphoton polarization entanglement,” Phys. Rev. Lett. 109, 080504 (2012).
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Shen Tu, G. L.

Y. Liu, L. Ju, X. L. Liang, S. B. Tang, G. L. Shen 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, 030501 (2012).
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Shenoy-Hejamadi, A.

A. Shenoy-Hejamadi and R. Srikanth, “Counterfactual distribution of Schrödinger cat states,” Phys. Rev. A 92, 062308 (2015).
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Shi, F.

F. Kong, C. Ju, P. Huang, P. Wang, X. Kong, F. Shi, L. Jiang, and J. Du, “Experimental realization of high-efficiency counterfactual computation,” Phys. Rev. Lett. 115, 080501 (2015).
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Srikanth, R.

A. Shenoy-Hejamadi and R. Srikanth, “Counterfactual distribution of Schrödinger cat states,” Phys. Rev. A 92, 062308 (2015).
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Tang, S. B.

Y. Liu, L. Ju, X. L. Liang, S. B. Tang, G. L. Shen 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, 030501 (2012).
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Traina, P.

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

D. D. Yavuz, P. B. Kulatunga, E. Urban, T. A. Johnson, N. Proite, T. Henage, T. G. Walker, and M. Saffman, “Fast ground state manipulation of neutral atoms in microscopic optical traps,” Phys. Rev. Lett. 96, 063001 (2006).
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Ursin, R.

X.-s. Ma, S. Zotter, J. Kofler, R. Ursin, T. Jennewein, C. Brukner, and A. Zeilinger, “Experimental delayed-choice entanglement swapping,” Nat. Phys. 8, 479–484 (2012).
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Vaidman, L.

L. Vaidman, “Comment on ‘Direct counterfactual transmission of a quantum state’,” Phys. Rev. A 93, 066301 (2016).
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L. Vaidman, “Counterfactuality of ‘counterfactual’ communication,” J. Phys. A: Math. Theor. 48, 465303 (2015).
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L. Vaidman, “Comment on ‘Protocol for direct counterfactual quantum communication’,” Phys. Rev. Lett. 112, 208901 (2014).
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L. Vaidman, “Impossibility of the counterfactual computation for all possible outcomes,” Phys. Rev. Lett. 98, 160403 (2007).
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A. C. Elitzur and L. Vaidman, “Quantum mechanical interaction-free measurements”, Found. Phys. 23, 987–997 (1993).
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Y. Aharonov and L. Vaidman, “Modification of ‘Counterfactual communication protocols’ which makes them truly counterfactual,” arXiv:1805.10634 (2018).

Vedral, V.

S. Bose, V. Vedral, and P. L. Knight, “Multiparticle generalization of entanglement swapping,” Phys. Rev. A 57, 822–829 (1998).
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Volz, J.

C. Junge, D. O’Shea, J. Volz, and A. Rauschenbeutel, “Strong coupling between single atoms and nontransversal photons,” Phys. Rev. Lett. 110, 213604 (2013).
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Wagenknecht, C.

A. M. Goebel, C. Wagenknecht, Q. Zhang, Y.-A. Chen, K. Chen, J. Schmiedmayer, and J.-W. Pan, “Multistage entanglement swapping,” Phys. Rev. Lett. 101, 080403 (2008).
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Walker, T. G.

D. D. Yavuz, P. B. Kulatunga, E. Urban, T. A. Johnson, N. Proite, T. Henage, T. G. Walker, and M. Saffman, “Fast ground state manipulation of neutral atoms in microscopic optical traps,” Phys. Rev. Lett. 96, 063001 (2006).
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Wang, H. F.

Q. Guo, L. Y. Cheng, L. Chen, H. F. Wang, and S. Zhang, “Counterfactual quantum-information transfer without transmitting any physical particles,” Sci. Rep. 5, 8416 (2015).
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Q. Guo, L. Y. Cheng, L. Chen, H. F. Wang, and S. Zhang, “Counterfactual entanglement distribution without transmitting any particles,” Opt. Express 22, 8970–8984 (2014).
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Wang, H.-F.

Q. Guo, S. Zhai, L.-Y. Cheng, H.-F. Wang, and S. Zhang, “Counterfactual quantum cloning without transmitting any physical particles,” Phys. Rev. A 96, 052335 (2017).
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Wang, P.

F. Kong, C. Ju, P. Huang, P. Wang, X. Kong, F. Shi, L. Jiang, and J. Du, “Experimental realization of high-efficiency counterfactual computation,” Phys. Rev. Lett. 115, 080501 (2015).
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Wang, S.

Z. Q. Yin, H. W. Li, Y. Yao, C. M. Zhang, S. Wang, W. Chen, G. C. Guo, and Z. F. Han, “Counterfactual quantum cryptography based on weak coherent states,” Phy. Rev. A 86, 022313 (2012).
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Weihs, G.

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, 4725–4728 (1999).
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Weinfurter, H.

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, 4725–4728 (1999).
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J.-W. Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental entanglement swapping: entangling photons that never interacted,” Phys. Rev. Lett. 80, 3891–3894 (1998).
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P. Kwiat, H. Weinfurter, T. Herzog, A. Zeilinger, and M. A. Kasevich, “Interaction-free measurement,” Phys. Rev. Lett. 74, 4763–4766 (1995).
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J. L. Zhang, F. Z. Guo, F. Gao, B. Liu, and Q. Y. Wen, “Private database queries based on counterfactual quantum key distribution,” Phys. Rev. A 88, 022334 (2013).
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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, 4725–4728 (1999).
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Xie, L.

Yao, Y.

Z. Q. Yin, H. W. Li, Y. Yao, C. M. Zhang, S. Wang, W. Chen, G. C. Guo, and Z. F. Han, “Counterfactual quantum cryptography based on weak coherent states,” Phy. Rev. A 86, 022313 (2012).
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D. D. Yavuz, P. B. Kulatunga, E. Urban, T. A. Johnson, N. Proite, T. Henage, T. G. Walker, and M. Saffman, “Fast ground state manipulation of neutral atoms in microscopic optical traps,” Phys. Rev. Lett. 96, 063001 (2006).
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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. USA 114, 4920 (2017).
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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. USA 114, 4920 (2017).
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Yin, Z. Q.

Z. Q. Yin, H. W. Li, Y. Yao, C. M. Zhang, S. Wang, W. Chen, G. C. Guo, and Z. F. Han, “Counterfactual quantum cryptography based on weak coherent states,” Phy. Rev. A 86, 022313 (2012).
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Z. Q. Yin, H. W. Li, W. Chen, Z. F. Han, and G. C. Guo, “Security of counterfactual quantum cryptography,” Phy. Rev. A 82, 042335 (2010).
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Zeilinger, A.

X.-s. Ma, S. Zotter, J. Kofler, R. Ursin, T. Jennewein, C. Brukner, and A. Zeilinger, “Experimental delayed-choice entanglement swapping,” Nat. Phys. 8, 479–484 (2012).
[Crossref]

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, 4725–4728 (1999).
[Crossref]

J.-W. Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental entanglement swapping: entangling photons that never interacted,” Phys. Rev. Lett. 80, 3891–3894 (1998).
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P. Kwiat, H. Weinfurter, T. Herzog, A. Zeilinger, and M. A. Kasevich, “Interaction-free measurement,” Phys. Rev. Lett. 74, 4763–4766 (1995).
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M. Zukowski, A. Zeilinger, M. A. Horne, and A. Ekert, “‘Event-Ready-Detectors’ Bell experiment via entanglement swapping,” Phys. Rev. Lett. 71, 4287–4290 (1993).
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Zhai, S.

Q. Guo, S. Zhai, L.-Y. Cheng, H.-F. Wang, and S. Zhang, “Counterfactual quantum cloning without transmitting any physical particles,” Phys. Rev. A 96, 052335 (2017).
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Zhang, C. M.

Z. Q. Yin, H. W. Li, Y. Yao, C. M. Zhang, S. Wang, W. Chen, G. C. Guo, and Z. F. Han, “Counterfactual quantum cryptography based on weak coherent states,” Phy. Rev. A 86, 022313 (2012).
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Zhang, J.

Zhang, J. L.

J. L. Zhang, F. Z. Guo, F. Gao, B. Liu, and Q. Y. Wen, “Private database queries based on counterfactual quantum key distribution,” Phys. Rev. A 88, 022334 (2013).
[Crossref]

Zhang, Q.

A. M. Goebel, C. Wagenknecht, Q. Zhang, Y.-A. Chen, K. Chen, J. Schmiedmayer, and J.-W. Pan, “Multistage entanglement swapping,” Phys. Rev. Lett. 101, 080403 (2008).
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Zhang, S.

Q. Guo, S. Zhai, L.-Y. Cheng, H.-F. Wang, and S. Zhang, “Counterfactual quantum cloning without transmitting any physical particles,” Phys. Rev. A 96, 052335 (2017).
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Q. Guo, L. Y. Cheng, L. Chen, H. F. Wang, and S. Zhang, “Counterfactual quantum-information transfer without transmitting any physical particles,” Sci. Rep. 5, 8416 (2015).
[Crossref] [PubMed]

Q. Guo, L. Y. Cheng, L. Chen, H. F. Wang, and S. Zhang, “Counterfactual entanglement distribution without transmitting any particles,” Opt. Express 22, 8970–8984 (2014).
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Zhou, L.

Y. Liu, L. Ju, X. L. Liang, S. B. Tang, G. L. Shen 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, 030501 (2012).
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Zhu, S.

Zoller, P.

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature (London) 414, 413–418 (2001).
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H.-J. Briegel, W. Dür, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81, 5932 (1998).
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Zotter, S.

X.-s. Ma, S. Zotter, J. Kofler, R. Ursin, T. Jennewein, C. Brukner, and A. Zeilinger, “Experimental delayed-choice entanglement swapping,” Nat. Phys. 8, 479–484 (2012).
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Zubairy, M. S.

Z. H. Li, M. Al-Amri, and M. S. Zubairy, “Direct counterfactual transmission of a quantum state,” Phys. Rev. A 92, 052315 (2015).
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Z. H. Li, M. Al-Amri, and M. S. Zubairy, “Direct quantum communication with almost invisible photons,” Phys. Rev. A 89, 052334 (2014).
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H. Salih, Z. H. Li, M. Al-Amri, and M. S. Zubairy, “Salih et al. Reply,” Phys. Rev. Lett. 112, 208902 (2014).
[Crossref]

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

M. Zukowski, A. Zeilinger, M. A. Horne, and A. Ekert, “‘Event-Ready-Detectors’ Bell experiment via entanglement swapping,” Phys. Rev. Lett. 71, 4287–4290 (1993).
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Found. Phys. (1)

A. C. Elitzur and L. Vaidman, “Quantum mechanical interaction-free measurements”, Found. Phys. 23, 987–997 (1993).
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J. Mod. Opt. (1)

A. Peres, “Delayed choice for entanglement swapping,” J. Mod. Opt. 47, 139–143 (2000).
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J. Phys. A: Math. Theor. (1)

L. Vaidman, “Counterfactuality of ‘counterfactual’ communication,” J. Phys. A: Math. Theor. 48, 465303 (2015).
[Crossref]

Laser Phys. Lett. (1)

G. Brida, A. Cavanna, I.P. Degiovanni, M. Genovese, and P. Traina, “Experimental realization of counterfactual quantum cryptography,” Laser Phys. Lett. 9, 247–252 (2012).
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Nat. Phys. (1)

X.-s. Ma, S. Zotter, J. Kofler, R. Ursin, T. Jennewein, C. Brukner, and A. Zeilinger, “Experimental delayed-choice entanglement swapping,” Nat. Phys. 8, 479–484 (2012).
[Crossref]

Nature (London) (3)

O. Hosten, M. T. Rakher, J. T. Barreiro, N. A. Peters, and P. G. Kwiat, “Counterfactual quantum computation through quantum interrogation,” Nature (London) 439, 949–952 (2006).
[Crossref]

A. Reiserer, N. Kalb, G. Rempe, and S. Ritter, “A quantum gate between a flying optical photon and a single trapped atom,” Nature (London) 508, 237–240 (2014).
[Crossref]

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature (London) 414, 413–418 (2001).
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Opt. Express (3)

Phy. Rev. A (2)

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

Z. Q. Yin, H. W. Li, Y. Yao, C. M. Zhang, S. Wang, W. Chen, G. C. Guo, and Z. F. Han, “Counterfactual quantum cryptography based on weak coherent states,” Phy. Rev. A 86, 022313 (2012).
[Crossref]

Phys. Rev. A (10)

J. L. Zhang, F. Z. Guo, F. Gao, B. Liu, and Q. Y. Wen, “Private database queries based on counterfactual quantum key distribution,” Phys. Rev. A 88, 022334 (2013).
[Crossref]

A. Shenoy-Hejamadi and R. Srikanth, “Counterfactual distribution of Schrödinger cat states,” Phys. Rev. A 92, 062308 (2015).
[Crossref]

Q. Guo, S. Zhai, L.-Y. Cheng, H.-F. Wang, and S. Zhang, “Counterfactual quantum cloning without transmitting any physical particles,” Phys. Rev. A 96, 052335 (2017).
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Z. H. Li, M. Al-Amri, and M. S. Zubairy, “Direct counterfactual transmission of a quantum state,” Phys. Rev. A 92, 052315 (2015).
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N. Gisin, “Optical communication without photons,” Phys. Rev. A 88, 030301 (2013).
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D. R. M. Arvidsson-Shukur and C. H. W. Barnes, “Quantum counterfactual communication without a weak trace,” Phys. Rev. A 94, 062303 (2016).
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Z. H. Li, M. Al-Amri, and M. S. Zubairy, “Direct quantum communication with almost invisible photons,” Phys. Rev. A 89, 052334 (2014).
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D. R. M. Arvidsson-Shukur, A. N. O. Gottfries, and C. H. W. Barnes, “Evaluation of counterfactuality in counterfactual communication protocols,” Phys. Rev. A 96, 062316 (2017).
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S. Bose, V. Vedral, and P. L. Knight, “Multiparticle generalization of entanglement swapping,” Phys. Rev. A 57, 822–829 (1998).
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L. Vaidman, “Comment on ‘Direct counterfactual transmission of a quantum state’,” Phys. Rev. A 93, 066301 (2016).
[Crossref]

Phys. Rev. Lett. (21)

L. Vaidman, “Comment on ‘Protocol for direct counterfactual quantum communication’,” Phys. Rev. Lett. 112, 208901 (2014).
[Crossref]

H. Salih, Z. H. Li, M. Al-Amri, and M. S. Zubairy, “Salih et al. Reply,” Phys. Rev. Lett. 112, 208902 (2014).
[Crossref]

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

M. Zukowski, A. Zeilinger, M. A. Horne, and A. Ekert, “‘Event-Ready-Detectors’ Bell experiment via entanglement swapping,” Phys. Rev. Lett. 71, 4287–4290 (1993).
[Crossref] [PubMed]

J.-W. Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental entanglement swapping: entangling photons that never interacted,” Phys. Rev. Lett. 80, 3891–3894 (1998).
[Crossref]

A. M. Goebel, C. Wagenknecht, Q. Zhang, Y.-A. Chen, K. Chen, J. Schmiedmayer, and J.-W. Pan, “Multistage entanglement swapping,” Phys. Rev. Lett. 101, 080403 (2008).
[Crossref] [PubMed]

E. Megidish, T. Shacham, A. Halevy, L. Dovrat, and H. S. Eisenberg, “Resource efficient source of multiphoton polarization entanglement,” Phys. Rev. Lett. 109, 080504 (2012).
[Crossref] [PubMed]

H.-J. Briegel, W. Dür, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81, 5932 (1998).
[Crossref]

E. Megidish, A. Halevy, T. Shacham, T. Dvir, L. Dovrat, and H. S. Eisenberg, “Entanglement swapping between photons that have never coexisted,” Phys. Rev. Lett. 110, 210403 (2013).
[Crossref] [PubMed]

L.-M. Duan and H. J. Kimble, “Scalable photonic quantum computation through cavity-assisted interactions,” Phys. Rev. Lett. 92, 127902 (2004).
[Crossref] [PubMed]

J. Cho and H.-W. Lee, “Generation of atomic cluster states through the cavity input-output process,” Phys. Rev. Lett. 95, 160501 (2005).
[Crossref] [PubMed]

L. Vaidman, “Impossibility of the counterfactual computation for all possible outcomes,” Phys. Rev. Lett. 98, 160403 (2007).
[Crossref] [PubMed]

F. Kong, C. Ju, P. Huang, P. Wang, X. Kong, F. Shi, L. Jiang, and J. Du, “Experimental realization of high-efficiency counterfactual computation,” Phys. Rev. Lett. 115, 080501 (2015).
[Crossref] [PubMed]

P. Kwiat, H. Weinfurter, T. Herzog, A. Zeilinger, and M. A. Kasevich, “Interaction-free measurement,” Phys. Rev. Lett. 74, 4763–4766 (1995).
[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, 4725–4728 (1999).
[Crossref]

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

Y. Liu, L. Ju, X. L. Liang, S. B. Tang, G. L. Shen 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, 030501 (2012).
[Crossref] [PubMed]

D. D. Yavuz, P. B. Kulatunga, E. Urban, T. A. Johnson, N. Proite, T. Henage, T. G. Walker, and M. Saffman, “Fast ground state manipulation of neutral atoms in microscopic optical traps,” Phys. Rev. Lett. 96, 063001 (2006).
[Crossref] [PubMed]

A. Boca, R. Miller, K. M. Birnbaum, A. D. Boozer, J. McKeever, and H. J. Kimble, “Observation of the vacuum rabi spectrum for one trapped atom,” Phys. Rev. Lett. 93, 233603 (2004).
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K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-not gate,” Phys. Rev. Lett. 93, 250502 (2004).
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C. Junge, D. O’Shea, J. Volz, and A. Rauschenbeutel, “Strong coupling between single atoms and nontransversal photons,” Phys. Rev. Lett. 110, 213604 (2013).
[Crossref] [PubMed]

Proc. Natl. Acad. Sci. USA (1)

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. USA 114, 4920 (2017).
[Crossref] [PubMed]

Rev. Mod. Phys. (1)

P. Kok, W. J. Munro, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[Crossref]

Sci. Rep. (1)

Q. Guo, L. Y. Cheng, L. Chen, H. F. Wang, and S. Zhang, “Counterfactual quantum-information transfer without transmitting any physical particles,” Sci. Rep. 5, 8416 (2015).
[Crossref] [PubMed]

Science (1)

A. Reiserer, S. Ritter, and G. Rempe, “Nondestructive detection of an optical photon,” Science 342, 1349 (2013).
[Crossref] [PubMed]

Other (3)

Y. Aharonov and L. Vaidman, “Modification of ‘Counterfactual communication protocols’ which makes them truly counterfactual,” arXiv:1805.10634 (2018).

H. Salih, W. McCutcheon, and J. Rarity, “Do the laws of physics prohibit counterfactual communication?” arXiv:1806.01257 (2018).

H. Salih, “From a quantum paradox to provably counterfactual disembodied transport: counterportation,” arXiv:1807.06586 (2018).

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Figures (6)

Fig. 1
Fig. 1 The quantum device for controlling the absorption or passing of a photon. MR: normal mirror. BS: 50:50 beam splitter. D: conventional photon detector. CM1 and CM2 compose a single-side cavity.
Fig. 2
Fig. 2 Schematic of the counterfactual entanglement swapping. PBS: polarizing beam splitter. SM: switchable mirror. SPR: switchable polarization rotator, where the arrow means SPR can only rotate the photon comes from the SM side. D: conventional photon detector. HWP: half-wave plate oriented at 22.5°. BS: 50:50 beam splitter. OD: optical delay line. AO: absorbing object used to absorb the photon from PBS2a(b).
Fig. 3
Fig. 3 The coefficients in Eq. (12) versus the different values of N and M. (a) x M 2 0, (b) xMyM → 0, (c) xMzM → 0, (d) y M 2 1, (e) yMzM → 1, (f) z M 2 1, with the increase of M and N.
Fig. 4
Fig. 4 The fidelity (a) and the probability (b) of obtaining Eqs. (13) or (18) versus values of outer and inner cycles M and N.
Fig. 5
Fig. 5 The fidelity (a) and the success probability (b) of the scheme versus the error coefficient s of the SPR for the different values of M and N.
Fig. 6
Fig. 6 The fidelity (a) and the success probability (b) of the scheme versus the photon loss rate γ for the different values of M and N.

Equations (21)

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| ψ = 1 2 ( | g g + | e e ) 12 ( | g g + | e e ) 34 | H 1 | H 2 .
| φ 1 2 cos ϑ ( | g g + | e e ) 12 | H 1 + 1 2 sin ϑ ( | g g + | e e ) 12 | V 1 .
| ϕ 1 2 ( | g g + | e e ) 12 ( cos θ | V 1 sin θ | H 1 ) .
| ϕ 1 2 cos θ ( | g g + | e e ) 12 | V 1 1 2 sin θ | e e 12 | H 1 .
| ϕ 1 2 [ cos N θ | g g 12 | V 1 + cos ( N θ ) | e e 12 | V 1 sin ( N θ ) | e e 12 | H 1 ] .
| ϕ 1 2 ( cos N π 2 N | g g 12 | V 1 | e e 12 | H 1 ) .
| φ 1 2 cos ϑ ( | g g + | e e ) 12 | H 1 + 1 2 sin ϑ ( cos N π 2 N | g g 12 | V 1 | e e 12 | H 1 ) .
| φ 1 2 cos ϑ ( | g g + | e e ) 12 | H 1 + 1 2 sin ϑ cos N π 2 N | g g 12 | V 1 .
| φ 1 2 ( x M | g g 12 | H 1 + y M | e e 12 | H 1 + z M | g g 12 | V 1 ) ,
x M = ( x M 1 cos ϑ z M 1 sin ϑ ) , y M = y M 1 cos ϑ , z M = ( z M 1 cos β 1 + x M 1 sin β 1 ) cos N θ ,
| φ 1 2 ( x M | g g 34 | H 2 + y M | e e 34 | H 2 + z M | g g 34 | V 2 ) ,
| ψ | φ | φ = 1 2 ( x M 2 | g g 12 | g g 34 | H 1 | H 2 + x M y M | g g 12 | e e 34 | H 1 | H 2 + x M z M | g g 12 | g g 34 | H 1 | V 2 + y M x M | e e 12 | g g 34 | H 1 | H 2 + y M 2 | e e 12 | e e 34 | H 1 | H 2 + y M z M | e e 12 | g g 34 | H 1 | V 2 + z M x M | g g 12 | g g 34 | V 1 | H 2 + z M y M | g g 12 | e e 34 | V 1 | H 2 + z M 2 | g g 12 | g g 34 | V 1 | V 2 ,
| ψ 1 2 ( | e e 12 | e e 34 | H 1 | H 2 + | e e 12 | g g 34 | H 1 | V 2 + | g g 12 | e e 34 | V 1 | H 2 + | g g 12 | g g 34 | V 1 | V 2 ) .
| ψ 1 2 ( | e e 12 | e e 34 | H 1 | H 2 + | g g 12 | g g 34 | V 1 | V 2 ) .
| ψ 1 2 ( | g g 12 | g g 34 + | e e 12 | e e 34 ) ,
| ψ 1 2 ( | g g 12 | g g 34 + | e e 12 | e e 34 ) .
| ψ 1 2 2 ( | g g 12 | g g 34 + | g g 12 | e g 34 + | e g 12 | g g 34 + | e g 12 | e g 34 + | g e 12 | g e 34 | g e 12 | e e 34 | e e 12 | g e 34 + | e e 12 | e e 34 ) .
| ψ 1 2 2 ( | e g 12 | e g 34 | H 3 | H 4 + | e e 12 | e e 34 | H 3 | H 4 + | g g 12 | e g 34 | V 3 | H 4 | g e 12 | e e 34 | V 3 | H 4 + | e g 12 | g g 34 | H 3 | V 4 | e e 12 | g e 34 | H 3 | V 4 + | g g 12 | g g 34 | V 3 | V 4 + | g e 12 | g e 34 | V 3 | V 4 ) .
| ψ 1 2 ( | e g 12 | e g 34 | H 3 | H 4 + | e e 12 | e e 34 | H 3 | H 4 + | g g 12 | g g 34 | V 3 | V 4 + | g e 12 | g e 34 | V 3 | V 4 ) .
| ψ 1 2 ( | g 1 | g 3 + | e 1 | e 3 ) ( | g 2 | g 4 + | e 2 | e 4 ) ,
| ψ 1 2 ( | g 1 | g 3 + | e 1 | e 3 ) ( | g 2 | g 4 + | e 2 | e 4 ) ,

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