Quantum Cloning of Steering

  • Received Date: April 13, 2022
  • Published Date: June 30, 2022
  • Quantum steering in a global state allows an observer to remotely steer a subsystem into different ensembles by performing different local measurements on the other part. We show that, in general, this property cannot be perfectly cloned by any joint operation between a steered subsystem and a third system. Perfect cloning is viable if and only if the initial state is of zero discord. We also investigate the process of cloning the steered qubit of a Bell state using a universal cloning machine. Einstein–Podolsky–Rosen (EPR) steering, which is a type of quantum correlation existing in the states without a local-hidden-state model, is observed in the two copy subsystems. This contradicts the conclusion of no-cloning of quantum steering (EPR steering) [C. Y. Chiu et al., npj Quantum Inf. 2, 16020 (2016)] based on a mutual information criterion for EPR steering.
  • Article Text

  • [1]
    Luo M X, Li H R, Lai H, and Wang X 2017 Quantum Inf. Process. 16 297 doi: 10.1007/s11128-017-1754-0

    CrossRef Google Scholar

    [2]
    Horodecki R, Horodecki P, Horodecki M, and Horodecki K 2009 Rev. Mod. Phys. 81 865 doi: 10.1103/RevModPhys.81.865

    CrossRef Google Scholar

    [3]
    Modi K, Brodutch A, Cable H, Paterek T, and Vedral V 2012 Rev. Mod. Phys. 84 1655 doi: 10.1103/RevModPhys.84.1655

    CrossRef Google Scholar

    [4]
    Brunner N, Cavalcanti D, Pironio S, Scarani V, and Wehner S 2014 Rev. Mod. Phys. 86 419 doi: 10.1103/RevModPhys.86.419

    CrossRef Google Scholar

    [5]
    Uola R, Costa A C, Nguyen H C, and Gühne O 2020 Rev. Mod. Phys. 92 015001 doi: 10.1103/RevModPhys.92.015001

    CrossRef Google Scholar

    [6]
    Nielsen M A and Chuang I L 2000 Quantum Computation and Quantum Information Cambridge: Cambridge University Press

    Google Scholar

    [7]
    Wootters W K and Zurek W H 1982 Nature 299 802 doi: 10.1038/299802a0

    CrossRef Google Scholar

    [8]
    Barnum H, Caves C M, Fuchs C A, Jozsa R, and Schumacher B 1996 Phys. Rev. Lett. 76 2818 doi: 10.1103/PhysRevLett.76.2818

    CrossRef Google Scholar

    [9]
    Pati A K and Braunstein S L 2000 Nature 404 164 doi: 10.1038/404130b0

    CrossRef Google Scholar

    [10]
    Pati A K and Braunstein S L 2003 arXiv:quant-ph/0303124

    Google Scholar

    [11]
    Modi K, Pati A K, Sen A, and Sen U 2018 Phys. Rev. Lett. 120 230501 doi: 10.1103/PhysRevLett.120.230501

    CrossRef Google Scholar

    [12]
    Bužek V and Hillery M 1996 Phys. Rev. A 54 1844 doi: 10.1103/PhysRevA.54.1844

    CrossRef Google Scholar

    [13]
    Scarani V, Iblisdir S, Gisin N, and Acin A 2005 Rev. Mod. Phys. 77 1225 doi: 10.1103/RevModPhys.77.1225

    CrossRef Google Scholar

    [14]
    Lamoureux L P, Navez P, Fiurášek J, and Cerf N J 2004 Phys. Rev. A 69 040301 doi: 10.1103/PhysRevA.69.040301

    CrossRef Google Scholar

    [15]
    Patel D, Patro S, Vanarasa C, Chakrabarty I, and Pati A K 2021 Phys. Rev. A 103 022422 doi: 10.1103/PhysRevA.103.022422

    CrossRef Google Scholar

    [16]
    Schrödinger E and I 1935 Mathematical Proceedings of the Cambridge Philosophical Society Cambridge: Cambridge University Press vol 31 p 555

    Google Scholar

    [17]
    Wiseman H M, Jones S J, and Doherty A C 2007 Phys. Rev. Lett. 98 140402 doi: 10.1103/PhysRevLett.98.140402

    CrossRef Google Scholar

    [18]
    Branciard C, Cavalcanti E G, Walborn S P, Scarani V, and Wiseman H M 2012 Phys. Rev. A 85 010301 doi: 10.1103/PhysRevA.85.010301

    CrossRef Google Scholar

    [19]
    Law Y Z, Thinh L P, Bancal J D, and Scarani V 2014 J. Phys. A 47 424028 doi: 10.1088/1751-8113/47/42/424028

    CrossRef Google Scholar

    [20]
    Peres A 1999 Found. Phys. 29 589 doi: 10.1023/A:1018816310000

    CrossRef Google Scholar

    [21]
    Vértesi T and Brunner N 2014 Nat. Commun. 5 5297 doi: 10.1038/ncomms6297

    CrossRef Google Scholar

    [22]
    Moroder T, Gittsovich O, Huber M, and Gühne O 2014 Phys. Rev. Lett. 113 050404 doi: 10.1103/PhysRevLett.113.050404

    CrossRef Google Scholar

    [23]
    Gisin N 1991 Phys. Lett. A 154 201 doi: 10.1016/0375-96019190805-I

    CrossRef Google Scholar

    [24]
    Chen J L, Su H Y, Xu Z P, Wu Y C, Wu C, Ye X J, Żukowski M, and Kwek L C 2015 Sci. Rep. 5 11624 doi: 10.1038/srep11624

    CrossRef Google Scholar

    [25]
    Cavalcanti D, Guerini L, Rabelo R, and Skrzypczyk P 2016 Phys. Rev. Lett. 117 190401 doi: 10.1103/PhysRevLett.117.190401

    CrossRef Google Scholar

    [26]
    Hirsch F, Quintino M T, Vértesi T, Pusey M F, and Brunner N 2016 Phys. Rev. Lett. 117 190402 doi: 10.1103/PhysRevLett.117.190402

    CrossRef Google Scholar

    [27]
    Zhu D, He G G, and Zhang F L 2022 Phys. Rev. A 105 062202 doi: 10.1103/PhysRevA.105.062202

    CrossRef Google Scholar

    [28]
    Chiu C Y, Lambert N, Liao T L, Nori F, and Li C M 2016 npj Quantum Inf. 2 16020 doi: 10.1038/npjqi.2016.20

    CrossRef Google Scholar

    [29]
    Li C M, Chen Y N, Lambert N, Chiu C Y, and Nori F 2015 Phys. Rev. A 92 062310 doi: 10.1103/PhysRevA.92.062310

    CrossRef Google Scholar

    [30]
    Jevtic S, Pusey M, Jennings D, and Rudolph T 2014 Phys. Rev. Lett. 113 020402 doi: 10.1103/PhysRevLett.113.020402

    CrossRef Google Scholar

    [31]
    Verstraete F 2002 Ph.D. Dissertation Katholieke Universiteit Leuven

    Google Scholar

    [32]
    Nguyen H C and Vu T 2016 Phys. Rev. A 94 012114 doi: 10.1103/PhysRevA.94.012114

    CrossRef Google Scholar

    [33]
    He G G, Fan X Y, and Zhang F L 2022 Mod. Phys. Lett. A 37 2250082 doi: 10.1142/S0217732322500821

    CrossRef Google Scholar

    [34]
    Jevtic S, Hall M J, Anderson M R, Zwierz M, and Wiseman H M 2015 J. Opt. Soc. Am. B 32 A40 doi: 10.1364/JOSAB.32.000A40

    CrossRef Google Scholar

    [35]
    Nguyen H C and Vu T 2016 Europhys. Lett. 115 10003 doi: 10.1209/0295-5075/115/10003

    CrossRef Google Scholar

    [36]
    Zhang F L and Zhang Y Y 2019 Phys. Rev. A 99 062314 doi: 10.1103/PhysRevA.99.062314

    CrossRef Google Scholar

    [37]
    Chitambar E, Streltsov A, Rana S, Bera M, Adesso G, and Lewenstein M 2016 Phys. Rev. Lett. 116 070402 doi: 10.1103/PhysRevLett.116.070402

    CrossRef Google Scholar

    [38]
    Matera J M, Egloff D, Killoran N, and Plenio M B 2016 Quantum Sci. Technol. 1 01LT01 doi: 10.1088/2058-9565/1/1/01LT01

    CrossRef Google Scholar

    [39]
    Streltsov A, Rana S, Bera M N, and Lewenstein M 2017 Phys. Rev. X 7 011024 doi: 10.1103/PhysRevX.7.011024

    CrossRef Google Scholar

    [40]
    Cerf N J 1999 Information-Theoretic Aspects of Quantum Copying. In: Williams C P eds Quantum Computing and Quantum Communications. QCQC 1998. Lecture Notes in Computer Science Berlin: Springer vol 1509 pp 218–234 doi: 10.1007/3-540-49208-9_19

    CrossRef Google Scholar

    [41]
    Cerf N J 2000 Phys. Rev. Lett. 84 4497 doi: 10.1103/PhysRevLett.84.4497

    CrossRef Google Scholar

    [42]
    Shang W M, Zhang F L, and Chen J L 2021 arXiv:2103.03126 [quant-ph]

    Google Scholar

    [43]
    Luo Y H, Zhong H S, Erhard M, Wang X L, Peng L C, Krenn M, Jiang X, Li L, Liu N L, Lu C Y et al.. 2019 Phys. Rev. Lett. 123 070505 doi: 10.1103/PhysRevLett.123.070505

    CrossRef Google Scholar

    [44]
    Hu X M, Zhang C, Liu B H, Cai Y, Ye X J, Guo Y, Xing W B, Huang C X, Huang Y F, Li C F et al.. 2020 Phys. Rev. Lett. 125 230501 doi: 10.1103/PhysRevLett.125.230501

    CrossRef Google Scholar

    [45]
    Liu Z H, Liang X B, Sun K, Li Q, Meng Y, Yang M, Li B, Chen J L, Xu J S, Li C F et al.. 2021 Phys. Rev. Lett. 126 170505 doi: 10.1103/PhysRevLett.126.170505

    CrossRef Google Scholar

    [46]
    Zhang R Q, Hou Z, Li Z, Zhu H, Xiang G Y, Li C F, and Guo G C 2021 Phys. Rev. Appl. 16 024052 doi: 10.1103/PhysRevApplied.16.024052

    CrossRef Google Scholar

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