Abstract

Asymmetric Einstein–Podolsky–Rosen (EPR) steering means the ability of one party to nonlocally “steer” the state in the other side through local measurements. The asymmetric property of EPR steering provides adequate security in one-sided device-independent secure quantum communication protocols. In this paper, we theoretically investigate the asymmetric EPR steering schemes between two subsystems of multipartite entangled states by an asymmetric modulation method. Two schemes, including tripartite entangled state to bipartite steering and quadripartite entangled state to tripartite steering, are investigated. By reconstructing the covariance matrix of continuous variable multipartite Gaussian states, we quantify the steerability of manipulating two different subsystems and demonstrate the EPR steering parameter versus various types of states’ parameters. Our work provides a reference for asymmetric quantum information processing and enriches resources for secure quantum networks.

© 2019 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
  29. W. X. Zhong, G. L. Cheng, and X. M. Hu, “One-way Einstein–Podolsky–Rosen steering with the aid of the thermal noise in a correlated emission laser,” Laser Phys. Lett. 15, 065204 (2018).
    [Crossref]
  30. Z. Huan, “Manipulating Einstein-Podolsky-Rosen steering by quantum-jump-based feedback in dissipative environment,” Int. J. Theor. Phys. 57, 3473–3479 (2018).
    [Crossref]
  31. M. H. Wang, Z. Z. Qin, and X. L. Su, “Swapping of Gaussian Einstein-Podolsky-Rosen steering,” Phys. Rev. A 95, 052311 (2017).
    [Crossref]
  32. M. H. Wang, Z. Z. Qin, Y. Wang, and X. L. Su, “Einstein-Podolsky-Rosen-steering swapping between two Gaussian multipartite entangled states,” Phys. Rev. A 96, 022307 (2017).
    [Crossref]
  33. I. Kogias, A. R. Lee, S. Ragy, and G. Adesso, “Quantification of Gaussian quantum steering,” Phys. Rev. Lett. 114, 060403 (2015).
    [Crossref]
  34. X. W. Deng, Y. Xiang, C. X. Tian, G. Adesso, Q. Y. He, Q. H. Gong, X. L. Su, C. D. Xie, and K. C. Peng, “Demonstration of monogamy relations for Einstein-Podolsky-Rosen steering in Gaussian cluster states,” Phys. Rev. Lett. 118, 230501 (2017).
    [Crossref]

2018 (3)

W. X. Zhong, G. L. Cheng, and X. M. Hu, “One-way Einstein–Podolsky–Rosen steering with the aid of the thermal noise in a correlated emission laser,” Laser Phys. Lett. 15, 065204 (2018).
[Crossref]

Z. Huan, “Manipulating Einstein-Podolsky-Rosen steering by quantum-jump-based feedback in dissipative environment,” Int. J. Theor. Phys. 57, 3473–3479 (2018).
[Crossref]

N. Tischler, F. Ghafari, T. J. Baker, S. Slussarenko, R. B. Patel, M. M. Weston, S. Wollmann, L. K. Shalm, V. B. Verma, S. W. Nam, H. C. Nguyen, H. M. Wiseman, and G. J. Pryde, “Conclusive experimental demonstration of one-way Einstein-Podolsky-Rosen steering,” Phys. Rev. Lett. 121, 100401 (2018).
[Crossref]

2017 (6)

Z. Z. Qin, X. W. Deng, C. X. Tian, M. H. Wang, X. L. Su, C. D. Xie, and K. C. Peng, “Manipulating the direction of Einstein-Podolsky-Rosen steering,” Phys. Rev. A 95, 052114 (2017).
[Crossref]

X. W. Deng, Y. Xiang, C. X. Tian, G. Adesso, Q. Y. He, Q. H. Gong, X. L. Su, C. D. Xie, and K. C. Peng, “Demonstration of monogamy relations for Einstein-Podolsky-Rosen steering in Gaussian cluster states,” Phys. Rev. Lett. 118, 230501 (2017).
[Crossref]

M. H. Wang, Z. Z. Qin, and X. L. Su, “Swapping of Gaussian Einstein-Podolsky-Rosen steering,” Phys. Rev. A 95, 052311 (2017).
[Crossref]

M. H. Wang, Z. Z. Qin, Y. Wang, and X. L. Su, “Einstein-Podolsky-Rosen-steering swapping between two Gaussian multipartite entangled states,” Phys. Rev. A 96, 022307 (2017).
[Crossref]

D. Cavalcanti and P. Skrzypczyk, “Quantum steering: a review with focus on semidefinite programming,” Rep. Prog. Phys. 80, 024001 (2017).
[Crossref]

Y. Xiang, I. Kogias, G. Adesso, and Q. Y. He, “Multipartite Gaussian steering: monogamy constraints and quantum cryptography application,” Phys. Rev. A 95, 010101 (2017).
[Crossref]

2016 (4)

C. Y. Chiu, N. Lambert, T. L. Liao, F. Nori, and C. M. Li, “No-cloning of quantum steering,” Npj Quantum Inf. 2, 16020 (2016).
[Crossref]

S. Wollmann, N. Walk, A. J. Bennet, H. M. Wiseman, and G. J. Pryde, “Observation of genuine one-way Einstein-Podolsky-Rosen steering,” Phys. Rev. Lett. 116, 160403 (2016).
[Crossref]

K. Sun, X. J. Ye, J. S. Xu, X. Y. Xu, J. S. Tang, Y. C. Wu, J. L. Chen, C. F. Li, and G. C. Guo, “Experimental quantification of asymmetric Einstein-Podolsky-Rosen steering,” Phys. Rev. Lett. 116, 160404 (2016).
[Crossref]

T. Guerreiro, F. Monteiro, A. Martin, J. B. Brask, T. Vértesi, B. Korzh, M. Caloz, F. Bussières, V. B. Verma, A. E. Lita, R. P. Mirin, S. W. Nam, F. Marsilli, M. D. Shaw, N. Gisin, N. Brunner, H. Zbinden, and R. T. Thew, “Demonstration of Einstein-Podolsky-Rosen steering using single-photon path entanglement and displacement-based detection,” Phys. Rev. Lett. 117, 070404 (2016).
[Crossref]

2015 (6)

M. T. Quintino, T. Vértesi, D. Cavalcanti, R. Augusiak, M. Demianowicz, A. Acín, and N. Brunner, “Inequivalence of entanglement, steering, and Bell nonlocality for general measurements,” Phys. Rev. A 92, 032107 (2015).
[Crossref]

I. Kogias, A. R. Lee, S. Ragy, and G. Adesso, “Quantification of Gaussian quantum steering,” Phys. Rev. Lett. 114, 060403 (2015).
[Crossref]

Q. Y. He, Q. H. Gong, and M. D. Reid, “Classifying directional Gaussian entanglement, Einstein-Podolsky-Rosen steering, and discord,” Phys. Rev. Lett. 114, 060402 (2015).
[Crossref]

L. Rosales-Zárate, R. Y. Teh, S. Kiesewetter, A. Brolis, K. Ng, and M. D. Reid, “Decoherence of Einstein-Podolsky-Rosen steering,” J. Opt. Soc. Am. B 32, A82–A91 (2015).
[Crossref]

S. J. Armstrong, M. Wang, R. Y. Teh, Q. H. Gong, Q. Y. He, J. R. Janousek, H. A. Bachor, M. D. Reid, and P. K. Lam, “Multipartite Einstein–Podolsky–Rosen steering and genuine tripartite entanglement with optical networks,” Nat. Phys. 11, 167–172 (2015).
[Crossref]

Q. He, L. Rosales-Zárate, G. Adesso, and M. D. Reid, “Secure continuous variable teleportation and Einstein-Podolsky-Rosen steering,” Phys. Rev. Lett. 115, 180502 (2015).
[Crossref]

2014 (2)

D. A. Evans and H. M. Wiseman, “Optimal measurements for tests of Einstein-Podolsky-Rosen steering with no detection loophole using two-qubit Werner states,” Phys. Rev. A 90, 012114 (2014).
[Crossref]

J. Bowles, T. Vértesi, M. T. Quintino, and N. Brunner, “One-way Einstein-Podolsky-Rosen steering,” Phys. Rev. Lett. 112, 200402 (2014).
[Crossref]

2013 (3)

C. Lee, S. Ji, and H. Nha, “Quantum steering for continuous variable states,” J. Opt. Soc. Am. B 30, 2483–2490 (2013).
[Crossref]

Q. Y. He and M. D. Reid, “Genuine multipartite Einstein Podolsky Rosen steering,” Phys. Rev. Lett. 111, 250403 (2013).
[Crossref]

M. D. Reid, “Signifying quantum benchmarks for qubit teleportation and secure quantum communication using Einstein-Podolsky-Rosen steering inequalities,” Phys. Rev. A 88, 062338 (2013).
[Crossref]

2012 (1)

V. Händchen, T. Eberle, S. Steinlechner, A. Samblowski, T. Franz, R. F. Werner, and R. Schnabel, “Observation of one-way Einstein–Podolsky–Rosen steering,” Nat. Photonics 6, 596–599 (2012).
[Crossref]

2010 (1)

S. L. W. Midgley, A. J. Ferris, and M. K. Olsen, “Asymmetric Gaussian steering: when Alice and Bob disagree,” Phys. Rev. A 81, 022101 (2010).
[Crossref]

2009 (2)

D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: the Einstein-Podolsky-Rosen paradox: from concepts to applications,” Rev. Mod. Phys. 81, 1727 (2009).
[Crossref]

R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, “Quantum entanglement,” Rev. Mod. Phys. 81, 865 (2009).
[Crossref]

2008 (1)

H. J. Kimble, “The quantum internet,” Nature 453, 1023–1030 (2008).
[Crossref]

2007 (1)

H. M. Wiseman, S. J. Jones, and A. C. Doherty, “Steering, entanglement, nonlocality, and the Einstein Podolsky Rosen paradox,” Phys. Rev. Lett. 98, 140402 (2007).
[Crossref]

1964 (1)

J. S. Bell, “On the Einstein Podolsky Rosen paradox,” Physics 1, 195–200 (1964).
[Crossref]

1936 (1)

E. Schrödinger, “Probability relations between separated systems,” Proc. Cambridge Philos. Soc. 32, 446–452 (1936).
[Crossref]

1935 (2)

E. Schrödinger, “Discussion of probability relations between separated systems,” Proc. Cambridge Philos. Soc 31, 555–563 (1935).
[Crossref]

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777 (1935).
[Crossref]

Acín, A.

M. T. Quintino, T. Vértesi, D. Cavalcanti, R. Augusiak, M. Demianowicz, A. Acín, and N. Brunner, “Inequivalence of entanglement, steering, and Bell nonlocality for general measurements,” Phys. Rev. A 92, 032107 (2015).
[Crossref]

Adesso, G.

Y. Xiang, I. Kogias, G. Adesso, and Q. Y. He, “Multipartite Gaussian steering: monogamy constraints and quantum cryptography application,” Phys. Rev. A 95, 010101 (2017).
[Crossref]

X. W. Deng, Y. Xiang, C. X. Tian, G. Adesso, Q. Y. He, Q. H. Gong, X. L. Su, C. D. Xie, and K. C. Peng, “Demonstration of monogamy relations for Einstein-Podolsky-Rosen steering in Gaussian cluster states,” Phys. Rev. Lett. 118, 230501 (2017).
[Crossref]

I. Kogias, A. R. Lee, S. Ragy, and G. Adesso, “Quantification of Gaussian quantum steering,” Phys. Rev. Lett. 114, 060403 (2015).
[Crossref]

Q. He, L. Rosales-Zárate, G. Adesso, and M. D. Reid, “Secure continuous variable teleportation and Einstein-Podolsky-Rosen steering,” Phys. Rev. Lett. 115, 180502 (2015).
[Crossref]

Andersen, U. L.

D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: the Einstein-Podolsky-Rosen paradox: from concepts to applications,” Rev. Mod. Phys. 81, 1727 (2009).
[Crossref]

Armstrong, S. J.

S. J. Armstrong, M. Wang, R. Y. Teh, Q. H. Gong, Q. Y. He, J. R. Janousek, H. A. Bachor, M. D. Reid, and P. K. Lam, “Multipartite Einstein–Podolsky–Rosen steering and genuine tripartite entanglement with optical networks,” Nat. Phys. 11, 167–172 (2015).
[Crossref]

Augusiak, R.

M. T. Quintino, T. Vértesi, D. Cavalcanti, R. Augusiak, M. Demianowicz, A. Acín, and N. Brunner, “Inequivalence of entanglement, steering, and Bell nonlocality for general measurements,” Phys. Rev. A 92, 032107 (2015).
[Crossref]

Bachor, H. A.

S. J. Armstrong, M. Wang, R. Y. Teh, Q. H. Gong, Q. Y. He, J. R. Janousek, H. A. Bachor, M. D. Reid, and P. K. Lam, “Multipartite Einstein–Podolsky–Rosen steering and genuine tripartite entanglement with optical networks,” Nat. Phys. 11, 167–172 (2015).
[Crossref]

D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: the Einstein-Podolsky-Rosen paradox: from concepts to applications,” Rev. Mod. Phys. 81, 1727 (2009).
[Crossref]

Baker, T. J.

N. Tischler, F. Ghafari, T. J. Baker, S. Slussarenko, R. B. Patel, M. M. Weston, S. Wollmann, L. K. Shalm, V. B. Verma, S. W. Nam, H. C. Nguyen, H. M. Wiseman, and G. J. Pryde, “Conclusive experimental demonstration of one-way Einstein-Podolsky-Rosen steering,” Phys. Rev. Lett. 121, 100401 (2018).
[Crossref]

Bell, J. S.

J. S. Bell, “On the Einstein Podolsky Rosen paradox,” Physics 1, 195–200 (1964).
[Crossref]

Bennet, A. J.

S. Wollmann, N. Walk, A. J. Bennet, H. M. Wiseman, and G. J. Pryde, “Observation of genuine one-way Einstein-Podolsky-Rosen steering,” Phys. Rev. Lett. 116, 160403 (2016).
[Crossref]

Bowen, W. P.

D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: the Einstein-Podolsky-Rosen paradox: from concepts to applications,” Rev. Mod. Phys. 81, 1727 (2009).
[Crossref]

Bowles, J.

J. Bowles, T. Vértesi, M. T. Quintino, and N. Brunner, “One-way Einstein-Podolsky-Rosen steering,” Phys. Rev. Lett. 112, 200402 (2014).
[Crossref]

Brask, J. B.

T. Guerreiro, F. Monteiro, A. Martin, J. B. Brask, T. Vértesi, B. Korzh, M. Caloz, F. Bussières, V. B. Verma, A. E. Lita, R. P. Mirin, S. W. Nam, F. Marsilli, M. D. Shaw, N. Gisin, N. Brunner, H. Zbinden, and R. T. Thew, “Demonstration of Einstein-Podolsky-Rosen steering using single-photon path entanglement and displacement-based detection,” Phys. Rev. Lett. 117, 070404 (2016).
[Crossref]

Brolis, A.

Brunner, N.

T. Guerreiro, F. Monteiro, A. Martin, J. B. Brask, T. Vértesi, B. Korzh, M. Caloz, F. Bussières, V. B. Verma, A. E. Lita, R. P. Mirin, S. W. Nam, F. Marsilli, M. D. Shaw, N. Gisin, N. Brunner, H. Zbinden, and R. T. Thew, “Demonstration of Einstein-Podolsky-Rosen steering using single-photon path entanglement and displacement-based detection,” Phys. Rev. Lett. 117, 070404 (2016).
[Crossref]

M. T. Quintino, T. Vértesi, D. Cavalcanti, R. Augusiak, M. Demianowicz, A. Acín, and N. Brunner, “Inequivalence of entanglement, steering, and Bell nonlocality for general measurements,” Phys. Rev. A 92, 032107 (2015).
[Crossref]

J. Bowles, T. Vértesi, M. T. Quintino, and N. Brunner, “One-way Einstein-Podolsky-Rosen steering,” Phys. Rev. Lett. 112, 200402 (2014).
[Crossref]

Bussières, F.

T. Guerreiro, F. Monteiro, A. Martin, J. B. Brask, T. Vértesi, B. Korzh, M. Caloz, F. Bussières, V. B. Verma, A. E. Lita, R. P. Mirin, S. W. Nam, F. Marsilli, M. D. Shaw, N. Gisin, N. Brunner, H. Zbinden, and R. T. Thew, “Demonstration of Einstein-Podolsky-Rosen steering using single-photon path entanglement and displacement-based detection,” Phys. Rev. Lett. 117, 070404 (2016).
[Crossref]

Caloz, M.

T. Guerreiro, F. Monteiro, A. Martin, J. B. Brask, T. Vértesi, B. Korzh, M. Caloz, F. Bussières, V. B. Verma, A. E. Lita, R. P. Mirin, S. W. Nam, F. Marsilli, M. D. Shaw, N. Gisin, N. Brunner, H. Zbinden, and R. T. Thew, “Demonstration of Einstein-Podolsky-Rosen steering using single-photon path entanglement and displacement-based detection,” Phys. Rev. Lett. 117, 070404 (2016).
[Crossref]

Cavalcanti, D.

D. Cavalcanti and P. Skrzypczyk, “Quantum steering: a review with focus on semidefinite programming,” Rep. Prog. Phys. 80, 024001 (2017).
[Crossref]

M. T. Quintino, T. Vértesi, D. Cavalcanti, R. Augusiak, M. Demianowicz, A. Acín, and N. Brunner, “Inequivalence of entanglement, steering, and Bell nonlocality for general measurements,” Phys. Rev. A 92, 032107 (2015).
[Crossref]

Cavalcanti, E. G.

D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: the Einstein-Podolsky-Rosen paradox: from concepts to applications,” Rev. Mod. Phys. 81, 1727 (2009).
[Crossref]

Chen, J. L.

K. Sun, X. J. Ye, J. S. Xu, X. Y. Xu, J. S. Tang, Y. C. Wu, J. L. Chen, C. F. Li, and G. C. Guo, “Experimental quantification of asymmetric Einstein-Podolsky-Rosen steering,” Phys. Rev. Lett. 116, 160404 (2016).
[Crossref]

Cheng, G. L.

W. X. Zhong, G. L. Cheng, and X. M. Hu, “One-way Einstein–Podolsky–Rosen steering with the aid of the thermal noise in a correlated emission laser,” Laser Phys. Lett. 15, 065204 (2018).
[Crossref]

Chiu, C. Y.

C. Y. Chiu, N. Lambert, T. L. Liao, F. Nori, and C. M. Li, “No-cloning of quantum steering,” Npj Quantum Inf. 2, 16020 (2016).
[Crossref]

Demianowicz, M.

M. T. Quintino, T. Vértesi, D. Cavalcanti, R. Augusiak, M. Demianowicz, A. Acín, and N. Brunner, “Inequivalence of entanglement, steering, and Bell nonlocality for general measurements,” Phys. Rev. A 92, 032107 (2015).
[Crossref]

Deng, X. W.

Z. Z. Qin, X. W. Deng, C. X. Tian, M. H. Wang, X. L. Su, C. D. Xie, and K. C. Peng, “Manipulating the direction of Einstein-Podolsky-Rosen steering,” Phys. Rev. A 95, 052114 (2017).
[Crossref]

X. W. Deng, Y. Xiang, C. X. Tian, G. Adesso, Q. Y. He, Q. H. Gong, X. L. Su, C. D. Xie, and K. C. Peng, “Demonstration of monogamy relations for Einstein-Podolsky-Rosen steering in Gaussian cluster states,” Phys. Rev. Lett. 118, 230501 (2017).
[Crossref]

Doherty, A. C.

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L. Rosales-Zárate, R. Y. Teh, S. Kiesewetter, A. Brolis, K. Ng, and M. D. Reid, “Decoherence of Einstein-Podolsky-Rosen steering,” J. Opt. Soc. Am. B 32, A82–A91 (2015).
[Crossref]

Thew, R. T.

T. Guerreiro, F. Monteiro, A. Martin, J. B. Brask, T. Vértesi, B. Korzh, M. Caloz, F. Bussières, V. B. Verma, A. E. Lita, R. P. Mirin, S. W. Nam, F. Marsilli, M. D. Shaw, N. Gisin, N. Brunner, H. Zbinden, and R. T. Thew, “Demonstration of Einstein-Podolsky-Rosen steering using single-photon path entanglement and displacement-based detection,” Phys. Rev. Lett. 117, 070404 (2016).
[Crossref]

Tian, C. X.

Z. Z. Qin, X. W. Deng, C. X. Tian, M. H. Wang, X. L. Su, C. D. Xie, and K. C. Peng, “Manipulating the direction of Einstein-Podolsky-Rosen steering,” Phys. Rev. A 95, 052114 (2017).
[Crossref]

X. W. Deng, Y. Xiang, C. X. Tian, G. Adesso, Q. Y. He, Q. H. Gong, X. L. Su, C. D. Xie, and K. C. Peng, “Demonstration of monogamy relations for Einstein-Podolsky-Rosen steering in Gaussian cluster states,” Phys. Rev. Lett. 118, 230501 (2017).
[Crossref]

Tischler, N.

N. Tischler, F. Ghafari, T. J. Baker, S. Slussarenko, R. B. Patel, M. M. Weston, S. Wollmann, L. K. Shalm, V. B. Verma, S. W. Nam, H. C. Nguyen, H. M. Wiseman, and G. J. Pryde, “Conclusive experimental demonstration of one-way Einstein-Podolsky-Rosen steering,” Phys. Rev. Lett. 121, 100401 (2018).
[Crossref]

Verma, V. B.

N. Tischler, F. Ghafari, T. J. Baker, S. Slussarenko, R. B. Patel, M. M. Weston, S. Wollmann, L. K. Shalm, V. B. Verma, S. W. Nam, H. C. Nguyen, H. M. Wiseman, and G. J. Pryde, “Conclusive experimental demonstration of one-way Einstein-Podolsky-Rosen steering,” Phys. Rev. Lett. 121, 100401 (2018).
[Crossref]

T. Guerreiro, F. Monteiro, A. Martin, J. B. Brask, T. Vértesi, B. Korzh, M. Caloz, F. Bussières, V. B. Verma, A. E. Lita, R. P. Mirin, S. W. Nam, F. Marsilli, M. D. Shaw, N. Gisin, N. Brunner, H. Zbinden, and R. T. Thew, “Demonstration of Einstein-Podolsky-Rosen steering using single-photon path entanglement and displacement-based detection,” Phys. Rev. Lett. 117, 070404 (2016).
[Crossref]

Vértesi, T.

T. Guerreiro, F. Monteiro, A. Martin, J. B. Brask, T. Vértesi, B. Korzh, M. Caloz, F. Bussières, V. B. Verma, A. E. Lita, R. P. Mirin, S. W. Nam, F. Marsilli, M. D. Shaw, N. Gisin, N. Brunner, H. Zbinden, and R. T. Thew, “Demonstration of Einstein-Podolsky-Rosen steering using single-photon path entanglement and displacement-based detection,” Phys. Rev. Lett. 117, 070404 (2016).
[Crossref]

M. T. Quintino, T. Vértesi, D. Cavalcanti, R. Augusiak, M. Demianowicz, A. Acín, and N. Brunner, “Inequivalence of entanglement, steering, and Bell nonlocality for general measurements,” Phys. Rev. A 92, 032107 (2015).
[Crossref]

J. Bowles, T. Vértesi, M. T. Quintino, and N. Brunner, “One-way Einstein-Podolsky-Rosen steering,” Phys. Rev. Lett. 112, 200402 (2014).
[Crossref]

Walk, N.

S. Wollmann, N. Walk, A. J. Bennet, H. M. Wiseman, and G. J. Pryde, “Observation of genuine one-way Einstein-Podolsky-Rosen steering,” Phys. Rev. Lett. 116, 160403 (2016).
[Crossref]

Wang, M.

S. J. Armstrong, M. Wang, R. Y. Teh, Q. H. Gong, Q. Y. He, J. R. Janousek, H. A. Bachor, M. D. Reid, and P. K. Lam, “Multipartite Einstein–Podolsky–Rosen steering and genuine tripartite entanglement with optical networks,” Nat. Phys. 11, 167–172 (2015).
[Crossref]

Wang, M. H.

Z. Z. Qin, X. W. Deng, C. X. Tian, M. H. Wang, X. L. Su, C. D. Xie, and K. C. Peng, “Manipulating the direction of Einstein-Podolsky-Rosen steering,” Phys. Rev. A 95, 052114 (2017).
[Crossref]

M. H. Wang, Z. Z. Qin, and X. L. Su, “Swapping of Gaussian Einstein-Podolsky-Rosen steering,” Phys. Rev. A 95, 052311 (2017).
[Crossref]

M. H. Wang, Z. Z. Qin, Y. Wang, and X. L. Su, “Einstein-Podolsky-Rosen-steering swapping between two Gaussian multipartite entangled states,” Phys. Rev. A 96, 022307 (2017).
[Crossref]

Wang, Y.

M. H. Wang, Z. Z. Qin, Y. Wang, and X. L. Su, “Einstein-Podolsky-Rosen-steering swapping between two Gaussian multipartite entangled states,” Phys. Rev. A 96, 022307 (2017).
[Crossref]

Werner, R. F.

V. Händchen, T. Eberle, S. Steinlechner, A. Samblowski, T. Franz, R. F. Werner, and R. Schnabel, “Observation of one-way Einstein–Podolsky–Rosen steering,” Nat. Photonics 6, 596–599 (2012).
[Crossref]

Weston, M. M.

N. Tischler, F. Ghafari, T. J. Baker, S. Slussarenko, R. B. Patel, M. M. Weston, S. Wollmann, L. K. Shalm, V. B. Verma, S. W. Nam, H. C. Nguyen, H. M. Wiseman, and G. J. Pryde, “Conclusive experimental demonstration of one-way Einstein-Podolsky-Rosen steering,” Phys. Rev. Lett. 121, 100401 (2018).
[Crossref]

Wiseman, H. M.

N. Tischler, F. Ghafari, T. J. Baker, S. Slussarenko, R. B. Patel, M. M. Weston, S. Wollmann, L. K. Shalm, V. B. Verma, S. W. Nam, H. C. Nguyen, H. M. Wiseman, and G. J. Pryde, “Conclusive experimental demonstration of one-way Einstein-Podolsky-Rosen steering,” Phys. Rev. Lett. 121, 100401 (2018).
[Crossref]

S. Wollmann, N. Walk, A. J. Bennet, H. M. Wiseman, and G. J. Pryde, “Observation of genuine one-way Einstein-Podolsky-Rosen steering,” Phys. Rev. Lett. 116, 160403 (2016).
[Crossref]

D. A. Evans and H. M. Wiseman, “Optimal measurements for tests of Einstein-Podolsky-Rosen steering with no detection loophole using two-qubit Werner states,” Phys. Rev. A 90, 012114 (2014).
[Crossref]

H. M. Wiseman, S. J. Jones, and A. C. Doherty, “Steering, entanglement, nonlocality, and the Einstein Podolsky Rosen paradox,” Phys. Rev. Lett. 98, 140402 (2007).
[Crossref]

Wollmann, S.

N. Tischler, F. Ghafari, T. J. Baker, S. Slussarenko, R. B. Patel, M. M. Weston, S. Wollmann, L. K. Shalm, V. B. Verma, S. W. Nam, H. C. Nguyen, H. M. Wiseman, and G. J. Pryde, “Conclusive experimental demonstration of one-way Einstein-Podolsky-Rosen steering,” Phys. Rev. Lett. 121, 100401 (2018).
[Crossref]

S. Wollmann, N. Walk, A. J. Bennet, H. M. Wiseman, and G. J. Pryde, “Observation of genuine one-way Einstein-Podolsky-Rosen steering,” Phys. Rev. Lett. 116, 160403 (2016).
[Crossref]

Wu, Y. C.

K. Sun, X. J. Ye, J. S. Xu, X. Y. Xu, J. S. Tang, Y. C. Wu, J. L. Chen, C. F. Li, and G. C. Guo, “Experimental quantification of asymmetric Einstein-Podolsky-Rosen steering,” Phys. Rev. Lett. 116, 160404 (2016).
[Crossref]

Xiang, Y.

Y. Xiang, I. Kogias, G. Adesso, and Q. Y. He, “Multipartite Gaussian steering: monogamy constraints and quantum cryptography application,” Phys. Rev. A 95, 010101 (2017).
[Crossref]

X. W. Deng, Y. Xiang, C. X. Tian, G. Adesso, Q. Y. He, Q. H. Gong, X. L. Su, C. D. Xie, and K. C. Peng, “Demonstration of monogamy relations for Einstein-Podolsky-Rosen steering in Gaussian cluster states,” Phys. Rev. Lett. 118, 230501 (2017).
[Crossref]

Xie, C. D.

X. W. Deng, Y. Xiang, C. X. Tian, G. Adesso, Q. Y. He, Q. H. Gong, X. L. Su, C. D. Xie, and K. C. Peng, “Demonstration of monogamy relations for Einstein-Podolsky-Rosen steering in Gaussian cluster states,” Phys. Rev. Lett. 118, 230501 (2017).
[Crossref]

Z. Z. Qin, X. W. Deng, C. X. Tian, M. H. Wang, X. L. Su, C. D. Xie, and K. C. Peng, “Manipulating the direction of Einstein-Podolsky-Rosen steering,” Phys. Rev. A 95, 052114 (2017).
[Crossref]

Xu, J. S.

K. Sun, X. J. Ye, J. S. Xu, X. Y. Xu, J. S. Tang, Y. C. Wu, J. L. Chen, C. F. Li, and G. C. Guo, “Experimental quantification of asymmetric Einstein-Podolsky-Rosen steering,” Phys. Rev. Lett. 116, 160404 (2016).
[Crossref]

Xu, X. Y.

K. Sun, X. J. Ye, J. S. Xu, X. Y. Xu, J. S. Tang, Y. C. Wu, J. L. Chen, C. F. Li, and G. C. Guo, “Experimental quantification of asymmetric Einstein-Podolsky-Rosen steering,” Phys. Rev. Lett. 116, 160404 (2016).
[Crossref]

Ye, X. J.

K. Sun, X. J. Ye, J. S. Xu, X. Y. Xu, J. S. Tang, Y. C. Wu, J. L. Chen, C. F. Li, and G. C. Guo, “Experimental quantification of asymmetric Einstein-Podolsky-Rosen steering,” Phys. Rev. Lett. 116, 160404 (2016).
[Crossref]

Zbinden, H.

T. Guerreiro, F. Monteiro, A. Martin, J. B. Brask, T. Vértesi, B. Korzh, M. Caloz, F. Bussières, V. B. Verma, A. E. Lita, R. P. Mirin, S. W. Nam, F. Marsilli, M. D. Shaw, N. Gisin, N. Brunner, H. Zbinden, and R. T. Thew, “Demonstration of Einstein-Podolsky-Rosen steering using single-photon path entanglement and displacement-based detection,” Phys. Rev. Lett. 117, 070404 (2016).
[Crossref]

Zhong, W. X.

W. X. Zhong, G. L. Cheng, and X. M. Hu, “One-way Einstein–Podolsky–Rosen steering with the aid of the thermal noise in a correlated emission laser,” Laser Phys. Lett. 15, 065204 (2018).
[Crossref]

Int. J. Theor. Phys. (1)

Z. Huan, “Manipulating Einstein-Podolsky-Rosen steering by quantum-jump-based feedback in dissipative environment,” Int. J. Theor. Phys. 57, 3473–3479 (2018).
[Crossref]

J. Opt. Soc. Am. B (2)

Laser Phys. Lett. (1)

W. X. Zhong, G. L. Cheng, and X. M. Hu, “One-way Einstein–Podolsky–Rosen steering with the aid of the thermal noise in a correlated emission laser,” Laser Phys. Lett. 15, 065204 (2018).
[Crossref]

Nat. Photonics (1)

V. Händchen, T. Eberle, S. Steinlechner, A. Samblowski, T. Franz, R. F. Werner, and R. Schnabel, “Observation of one-way Einstein–Podolsky–Rosen steering,” Nat. Photonics 6, 596–599 (2012).
[Crossref]

Nat. Phys. (1)

S. J. Armstrong, M. Wang, R. Y. Teh, Q. H. Gong, Q. Y. He, J. R. Janousek, H. A. Bachor, M. D. Reid, and P. K. Lam, “Multipartite Einstein–Podolsky–Rosen steering and genuine tripartite entanglement with optical networks,” Nat. Phys. 11, 167–172 (2015).
[Crossref]

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[Crossref]

Npj Quantum Inf. (1)

C. Y. Chiu, N. Lambert, T. L. Liao, F. Nori, and C. M. Li, “No-cloning of quantum steering,” Npj Quantum Inf. 2, 16020 (2016).
[Crossref]

Phys. Rev. (1)

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[Crossref]

Phys. Rev. A (8)

Y. Xiang, I. Kogias, G. Adesso, and Q. Y. He, “Multipartite Gaussian steering: monogamy constraints and quantum cryptography application,” Phys. Rev. A 95, 010101 (2017).
[Crossref]

M. D. Reid, “Signifying quantum benchmarks for qubit teleportation and secure quantum communication using Einstein-Podolsky-Rosen steering inequalities,” Phys. Rev. A 88, 062338 (2013).
[Crossref]

Z. Z. Qin, X. W. Deng, C. X. Tian, M. H. Wang, X. L. Su, C. D. Xie, and K. C. Peng, “Manipulating the direction of Einstein-Podolsky-Rosen steering,” Phys. Rev. A 95, 052114 (2017).
[Crossref]

M. T. Quintino, T. Vértesi, D. Cavalcanti, R. Augusiak, M. Demianowicz, A. Acín, and N. Brunner, “Inequivalence of entanglement, steering, and Bell nonlocality for general measurements,” Phys. Rev. A 92, 032107 (2015).
[Crossref]

D. A. Evans and H. M. Wiseman, “Optimal measurements for tests of Einstein-Podolsky-Rosen steering with no detection loophole using two-qubit Werner states,” Phys. Rev. A 90, 012114 (2014).
[Crossref]

S. L. W. Midgley, A. J. Ferris, and M. K. Olsen, “Asymmetric Gaussian steering: when Alice and Bob disagree,” Phys. Rev. A 81, 022101 (2010).
[Crossref]

M. H. Wang, Z. Z. Qin, and X. L. Su, “Swapping of Gaussian Einstein-Podolsky-Rosen steering,” Phys. Rev. A 95, 052311 (2017).
[Crossref]

M. H. Wang, Z. Z. Qin, Y. Wang, and X. L. Su, “Einstein-Podolsky-Rosen-steering swapping between two Gaussian multipartite entangled states,” Phys. Rev. A 96, 022307 (2017).
[Crossref]

Phys. Rev. Lett. (11)

I. Kogias, A. R. Lee, S. Ragy, and G. Adesso, “Quantification of Gaussian quantum steering,” Phys. Rev. Lett. 114, 060403 (2015).
[Crossref]

X. W. Deng, Y. Xiang, C. X. Tian, G. Adesso, Q. Y. He, Q. H. Gong, X. L. Su, C. D. Xie, and K. C. Peng, “Demonstration of monogamy relations for Einstein-Podolsky-Rosen steering in Gaussian cluster states,” Phys. Rev. Lett. 118, 230501 (2017).
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Q. Y. He, Q. H. Gong, and M. D. Reid, “Classifying directional Gaussian entanglement, Einstein-Podolsky-Rosen steering, and discord,” Phys. Rev. Lett. 114, 060402 (2015).
[Crossref]

T. Guerreiro, F. Monteiro, A. Martin, J. B. Brask, T. Vértesi, B. Korzh, M. Caloz, F. Bussières, V. B. Verma, A. E. Lita, R. P. Mirin, S. W. Nam, F. Marsilli, M. D. Shaw, N. Gisin, N. Brunner, H. Zbinden, and R. T. Thew, “Demonstration of Einstein-Podolsky-Rosen steering using single-photon path entanglement and displacement-based detection,” Phys. Rev. Lett. 117, 070404 (2016).
[Crossref]

J. Bowles, T. Vértesi, M. T. Quintino, and N. Brunner, “One-way Einstein-Podolsky-Rosen steering,” Phys. Rev. Lett. 112, 200402 (2014).
[Crossref]

N. Tischler, F. Ghafari, T. J. Baker, S. Slussarenko, R. B. Patel, M. M. Weston, S. Wollmann, L. K. Shalm, V. B. Verma, S. W. Nam, H. C. Nguyen, H. M. Wiseman, and G. J. Pryde, “Conclusive experimental demonstration of one-way Einstein-Podolsky-Rosen steering,” Phys. Rev. Lett. 121, 100401 (2018).
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Q. He, L. Rosales-Zárate, G. Adesso, and M. D. Reid, “Secure continuous variable teleportation and Einstein-Podolsky-Rosen steering,” Phys. Rev. Lett. 115, 180502 (2015).
[Crossref]

S. Wollmann, N. Walk, A. J. Bennet, H. M. Wiseman, and G. J. Pryde, “Observation of genuine one-way Einstein-Podolsky-Rosen steering,” Phys. Rev. Lett. 116, 160403 (2016).
[Crossref]

K. Sun, X. J. Ye, J. S. Xu, X. Y. Xu, J. S. Tang, Y. C. Wu, J. L. Chen, C. F. Li, and G. C. Guo, “Experimental quantification of asymmetric Einstein-Podolsky-Rosen steering,” Phys. Rev. Lett. 116, 160404 (2016).
[Crossref]

Q. Y. He and M. D. Reid, “Genuine multipartite Einstein Podolsky Rosen steering,” Phys. Rev. Lett. 111, 250403 (2013).
[Crossref]

H. M. Wiseman, S. J. Jones, and A. C. Doherty, “Steering, entanglement, nonlocality, and the Einstein Podolsky Rosen paradox,” Phys. Rev. Lett. 98, 140402 (2007).
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D. Cavalcanti and P. Skrzypczyk, “Quantum steering: a review with focus on semidefinite programming,” Rep. Prog. Phys. 80, 024001 (2017).
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[Crossref]

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Figures (4)

Fig. 1.
Fig. 1. Schematic of physical system for manipulating the direction of EPR steering. (a) Scheme for the asymmetric EPR steering between two modes; (b) scheme for the asymmetric EPR steering between tripartite modes. $ {{\rm BS}_{1 - 4}} $ denote beam splitters; $ {T_{1 - 4}} $ are the transmissivity of the beam splitters; $ i $ and $ - 1 $ denote 90° and 180° rotation in phase space of the corresponding mode; EOMp and EOMx, phase and amplitude electro-optical modulators; $ {{\rm HD}_{1 - 5}} $ are homodyne detectors.
Fig. 2.
Fig. 2. Asymmetric EPR steering parameter between two modes in Scheme 1. (a) EPR steering versus the gain factor $ {g_2} $ between $ B^\prime $ and $ C^\prime $ with squeezing parameter $ r = r_0 = 0.57 $ and the gain factor $g_1 = 1$ ; (b) EPR steering versus squeezing parameter $r$ between $ B^\prime $ and $ C^\prime $ with $ r_0 = 0.57 $ , $ g_1 = 1 $ , and $ g_2 = 0.7 $ .
Fig. 3.
Fig. 3. Asymmetric EPR steering parameter between any two modes in Scheme 2. (a) and (b) EPR steering does not exist between $ B^\prime $ and $ C^\prime $ (between $ B^\prime $ and $ D $ ). (c) EPR steering versus the gain factor $ g_2 $ between $ C^\prime $ and $ D $ with $ r = r_0 = 0.57 $ and $ g_1 = 1 $ ; (d) EPR steering versus squeezing parameter $ r $ between $ C^\prime $ and $ D $ with $ r_0 = 0.57 $ , $ g_1 = 1$ , and $ g_2 = 0.4 $ .
Fig. 4.
Fig. 4. Asymmetric EPR steering parameter between one and another two modes in Scheme 2. (a) EPR steering versus the gain factor $ g_2 $ between $ B^\prime $ mode and $ \{ C^\prime , D \} $ mode with $r = r_0 = 0.57$ and $g_1 = 1$ ; (b) EPR steering versus squeezing parameter $r$ between $ B^\prime $ and $ \{ C^\prime, D \} $ with $r_0 = 0.57$ , $ g_1 = 1$ , and $g_2 = 0.2$ ; (c) EPR steering versus the gain factor $g_2$ between $ C^\prime $ mode and $ \{ B^\prime , D \} $ mode with $r = r_0 = 0.57$ and $g_1 = 1$ ; (d) EPR steering versus squeezing parameter $r$ between $ C^\prime $ and $ \{ B^\prime , D \} $ with $r_0 = 0.57$ , $g_1 = 1$ , and $g_2 = 0.5$ ; (e) EPR steering versus the gain factor $g_2$ between $ D $ mode and $ \{ B^\prime ,C^\prime \} $ mode with $r = r_0 = 0.57$ and $g_1 = 1$ ; (f) EPR steering versus squeezing parameter $r$ between $ D $ and $ \{ B^\prime ,C^\prime \} $ with $r_0 = 0.57$ , $g_1 = 1$ , and $g_2 = 0.5$ .

Equations (14)

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σ A B = ( A C C T B ) ,
σ i j = C o v ( ξ i , ξ j ) = ξ i ξ j + ξ j ξ i / 2 ξ i ξ j ,
G A B ( σ A B ) = m a x { 0 , j : ν ¯ j A B A < 1 I n ( ν ¯ j A B A ) } ,
a ^ 1 = 1 2 [ e r 1 x ^ 1 ( 0 ) + i e r 1 p ^ 1 ( 0 ) ] , a ^ 2 = 1 2 [ e r 2 x ^ 2 ( 0 ) + i e r 2 p ^ 2 ( 0 ) ] , a ^ 3 = 1 2 [ e r 3 x ^ 3 ( 0 ) + i e r 3 p ^ 3 ( 0 ) ] ,
A ^ = 2 3 a ^ 1 + 1 3 a ^ 2 , B ^ = 1 6 a ^ 1 + 1 3 a ^ 2 + 1 2 a ^ 3 , C ^ = 1 6 a ^ 1 + 1 3 a ^ 2 1 2 a ^ 3
E ^ = 1 2 ( A ^ + a ^ i n ) , F ^ = 1 2 ( A ^ a ^ i n ) .
B ^ = B ^ + g 1 x ^ E + i g 1 p ^ F , C ^ = C ^ + g 2 x ^ E ,
x ^ B , = ( 1 6 1 3 g 1 ) e r x ^ 1 ( 0 ) + ( 1 3 + 1 6 g 1 ) e r x ^ 2 ( 0 ) + 1 2 e r x ^ 3 ( 0 ) + 1 2 g 1 e r 0 x ^ i n ( 0 ) , p ^ B = ( 1 6 1 3 g 1 ) e r p ^ 1 ( 0 ) + ( 1 3 + 1 6 g 1 ) e r p ^ 2 ( 0 ) + 1 2 e r p ^ 3 ( 0 ) 1 2 g 1 e r 0 p ^ i n ( 0 ) , x ^ C = ( 1 6 1 3 g 2 ) e r x ^ 1 ( 0 ) + ( 1 3 + 1 6 g 2 ) e r x ^ 2 ( 0 ) 1 2 e r x ^ 3 ( 0 ) + 1 2 g 2 e r 0 x ^ i n ( 0 ) , p ^ C = 1 6 e r p ^ 1 ( 0 ) + 1 3 e r p ^ 2 ( 0 ) + 1 2 e r p ^ 3 ( 0 ) .
σ B = [ Δ 2 x ^ B 0 0 Δ 2 p ^ B ] , σ C = [ Δ 2 x ^ C 0 0 Δ 2 p ^ C ] , σ B C = [ C o v ( x ^ B , x ^ C ) C o v ( x ^ B , p ^ C ) C o v ( p ^ B , x ^ C ) C o v ( p ^ B , p ^ C ) ] .
σ = [ σ B σ B C σ B C T σ C ] .
a ^ 1 = 1 2 [ e r 1 x ^ 1 ( 0 ) + i e r 1 p ^ 1 ( 0 ) ] , a ^ 2 = 1 2 [ e r 2 x ^ 2 ( 0 ) + i e r 2 p ^ 2 ( 0 ) ] , a ^ 3 = 1 2 [ e r 3 x ^ 3 ( 0 ) + i e r 3 p ^ 3 ( 0 ) ] , a ^ 4 = 1 2 [ e r 4 x ^ 4 ( 0 ) + i e r 4 p ^ 4 ( 0 ) ] .
A ^ = 1 2 a ^ 1 2 5 a ^ 2 i 1 10 a ^ 3 , B ^ = 1 2 a ^ 1 2 5 a ^ 2 i 1 10 a ^ 3 , C ^ = i 1 10 a ^ 2 + 2 5 a ^ 3 1 2 a ^ 4 , D ^ = i 1 10 a ^ 2 + 2 5 a ^ 3 + 1 2 a ^ 4 .
E ^ = 1 2 ( A ^ + a ^ i n ) , F ^ = 1 2 ( A ^ a ^ i n ) .
B ^ = B ^ + g 1 x ^ E + i g 1 p ^ F , C ^ = C ^ + g 2 x ^ E , D ^ = i 1 10 a ^ 2 + 2 5 a ^ 3 + 1 2 a ^ 4 ,

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