Contextual advantage for state-dependent cloning

Matteo Lostaglio1,2 and Gabriel Senno1

1ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels (Barcelona), 08860, Spain
2QuTech, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands

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A number of noncontextual models exist which reproduce different subsets of quantum theory and admit a no-cloning theorem. Therefore, if one chooses noncontextuality as one's notion of classicality, no-cloning cannot be regarded as a nonclassical phenomenon. In this work, however, we show that there are aspects of the phenomenology of quantum state cloning which are indeed nonclassical according to this principle. Specifically, we focus on the task of state-dependent cloning and prove that the optimal cloning fidelity predicted by quantum theory cannot be explained by any noncontextual model. We derive a noise-robust noncontextuality inequality whose violation by quantum theory not only implies a quantum advantage for the task of state-dependent cloning relative to noncontextual models, but also provides an experimental witness of noncontextuality.

It has been known for 50 years now that quantum information, differently from classical information, cannot be cloned. However, as we have learned in the last years, this $\textit{a priori}$ genuine quantum feature can be perfectly emulated classically by imagining that, when we experimentally prepare a quantum state, what is "really" going on is that we are preparing one of many ontic (a.k.a. hidden) states according to some probability distribution. If overlapping quantum states correspond to overlapping probability distributions, then we obtain a simple explanation of the no-cloning theorem. So, one may wonder, is there anything truly nonclassical in the phenomenology of quantum cloning?

In this work, we studied this question in terms of how well quantum mechanics clones a given pair of (in general) overlapping states, using a set of fundamental results worked out during the hey-days of quantum information theory. We showed that the tradeoff between the fidelity of the input pair and that of the (necessarily) imperfect clones is too good in quantum theory to be explainable in terms of the overlap of probabilities over some classical states. Specifically, we showed that $contextuality$, already identified as a necessary resource for universal quantum computation and optimal state discrimination, is what allows quantum mechanics to clone better than one can anticipate from classical emulations. Our main contribution is a noise-robust noncontextuality inequality whose violation by quantum theory not only $\textit{implies a quantum advantage for the task of state-dependent cloning}$ but also provides an experimental witness of noncontextuality. We expect our methods to be suitable to identify nonclassicality in other quantum phenomena such as, e.g., quantum teleportation.

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[1] William K Wootters and Wojciech H Zurek. A single quantum cannot be cloned. Nature, 299 (5886): 802, 1982. 10.1038/​299802a0.

[2] D Dieks. Communication by EPR devices. Physics Letters A, 92 (6): 271–272, 1982. 10.1016/​0375-9601(82)90084-6.

[3] James L Park. The concept of transition in quantum mechanics. Foundations of Physics, 1 (1): 23–33, 1970. 10.1007/​BF00708652.

[4] Horace P Yuen. Amplification of quantum states and noiseless photon amplifiers. Physics Letters A, 113 (8): 405–407, 1986. 10.1016/​0375-9601(86)90660-2.

[5] David Schmid and Robert W Spekkens. Contextual advantage for state discrimination. Physical Review X, 8 (1): 011015, 2018. 10.1103/​PhysRevX.8.011015.

[6] Robert W Spekkens. Contextuality for preparations, transformations, and unsharp measurements. Physical Review A, 71 (5): 052108, 2005. 10.1103/​PhysRevA.71.052108.

[7] Stephen D Bartlett, Terry Rudolph, and Robert W Spekkens. Reconstruction of Gaussian quantum mechanics from Liouville mechanics with an epistemic restriction. Physical Review A, 86 (1): 012103, 2012. 10.1103/​PhysRevA.86.012103.

[8] Robert W Spekkens. Evidence for the epistemic view of quantum states: A toy theory. Physical Review A, 75 (3): 032110, 2007. 10.1103/​PhysRevA.75.032110.

[9] A Daffertshofer, AR Plastino, and A Plastino. Classical no-cloning theorem. Physical review letters, 88 (21): 210601, 2002. 10.1103/​PhysRevLett.88.210601.

[10] Vladimir Bužek and Mark Hillery. Quantum copying: Beyond the no-cloning theorem. Physical Review A, 54 (3): 1844, 1996. 10.1103/​PhysRevA.54.1844.

[11] Valerio Scarani, Sofyan Iblisdir, Nicolas Gisin, and Antonio Acín. Quantum cloning. Rev. Mod. Phys., 77: 1225–1256, Nov 2005. 10.1103/​RevModPhys.77.1225.

[12] Debashis Saha, Paweł Horodecki, and Marcin Pawłowski. State independent contextuality advances one-way communication. New Journal of Physics, 21 (9): 093057, 2019. 10.1088/​1367-2630/​ab4149.

[13] Armin Tavakoli and Roope Uola. Measurement incompatibility and steering are necessary and sufficient for operational contextuality. Phys. Rev. Research, 2: 013011, Jan 2020. 10.1103/​PhysRevResearch.2.013011.

[14] Matthew Saul Leifer. Is the quantum state real? an extended review of $\psi$-ontology theorems. Quanta, 3 (1): 67–155, 2014. 10.12743/​quanta.v3i1.22.

[15] Simon Kochen and Ernst P Specker. The problem of hidden variables in quantum mechanics. In The logico-algebraic approach to quantum mechanics, pages 293–328. Springer, 1975. 10.1007/​978-94-010-1795-4_17.

[16] Robert W Spekkens. The ontological identity of empirical indiscernibles: Leibniz's methodological principle and its significance in the work of Einstein. 2019. URL https:/​/​​abs/​1909.04628v1.

[17] Dagmar Bruß, David P DiVincenzo, Artur Ekert, Christopher A Fuchs, Chiara Macchiavello, and John A Smolin. Optimal universal and state-dependent quantum cloning. Physical Review A, 57 (4): 2368, 1998. 10.1103/​PhysRevA.57.2368.

[18] Matthew S Leifer and Owen JE Maroney. Maximally epistemic interpretations of the quantum state and contextuality. Physical review letters, 110 (12): 120401, 2013. 10.1103/​PhysRevLett.110.120401.

[19] Matthew F Pusey, Jonathan Barrett, and Terry Rudolph. On the reality of the quantum state. Nature Physics, 8 (6): 475–478, 2012. 10.1038/​nphys2309.

[20] Michael D. Mazurek, Matthew F. Pusey, Ravi Kunjwal, Kevin J. Resch, and Robert W. Spekkens. An experimental test of noncontextuality without unphysical idealizations. Nat. Commun., 7: 11780, Jun 2016. 10.1038/​ncomms11780.

[21] Matthew F. Pusey, Lídia del Rio, and Bettina Meyer. Contextuality without access to a tomographically complete set, 2019. URL https:/​/​​abs/​1904.08699v1.

[22] Valerio Scarani, Helle Bechmann-Pasquinucci, Nicolas J Cerf, Miloslav Dušek, Norbert Lütkenhaus, and Momtchil Peev. The security of practical quantum key distribution. Reviews of modern physics, 81 (3): 1301, 2009. 10.1103/​RevModPhys.81.1301.

[23] P Deuar and WJ Munro. Quantum copying can increase the practically available information. Physical Review A, 62 (4): 042304, 2000. 10.1103/​PhysRevA.62.042304.

Cited by

[1] Ana Belén Sainz, "What is non-classical about quantum no-cloning?", Quantum Views 4, 39 (2020).

[2] David Schmid, John Selby, Elie Wolfe, Ravi Kunjwal, and Robert W. Spekkens, "The Characterization of Noncontextuality in the Framework of Generalized Probabilistic Theories", arXiv:1911.10386.

[3] Matteo Lostaglio, "Certifying quantum signatures in thermodynamics and metrology via contextuality of quantum linear response", arXiv:2004.01213.

[4] David Schmid, John H. Selby, Matthew F. Pusey, and Robert W. Spekkens, "A structure theorem for generalized-noncontextual ontological models", arXiv:2005.07161.

The above citations are from Crossref's cited-by service (last updated successfully 2020-08-07 16:36:59) and SAO/NASA ADS (last updated successfully 2020-08-07 16:37:00). The list may be incomplete as not all publishers provide suitable and complete citation data.

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