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.

[1] Lorenzo Catani, Ricardo Faleiro, Pierre-Emmanuel Emeriau, Shane Mansfield, and Anna Pappa, "Connecting xor and xor * games", Physical Review A 109 1, 012427 (2024).

[2] Roberto D. Baldijão, Rafael Wagner, Cristhiano Duarte, Bárbara Amaral, and Marcelo Terra Cunha, "Emergence of Noncontextuality under Quantum Darwinism", PRX Quantum 2 3, 030351 (2021).

[3] Matteo Lostaglio, "Certifying Quantum Signatures in Thermodynamics and Metrology via Contextuality of Quantum Linear Response", Physical Review Letters 125 23, 230603 (2020).

[4] David Schmid, John H. Selby, Matthew F. Pusey, and Robert W. Spekkens, "A structure theorem for generalized-noncontextual ontological models", Quantum 8, 1283 (2024).

[5] Massy Khoshbin, Lorenzo Catani, and Matthew Leifer, "Alternative robust ways of witnessing nonclassicality in the simplest scenario", Physical Review A 109 3, 032212 (2024).

[6] Rafael Wagner, Roberto D Baldijão, Alisson Tezzin, and Bárbara Amaral, "Using a resource theoretic perspective to witness and engineer quantum generalized contextuality for prepare-and-measure scenarios", Journal of Physics A: Mathematical and Theoretical 56 50, 505303 (2023).

[7] Armin Tavakoli, Emmanuel Zambrini Cruzeiro, Roope Uola, and Alastair A. Abbott, "Bounding and Simulating Contextual Correlations in Quantum Theory", PRX Quantum 2 2, 020334 (2021).

[8] Abhyoudai S. S., Sumit Mukherjee, and A. K. Pan, "Robust certification of unsharp instruments through sequential quantum advantages in a prepare-measure communication game", Physical Review A 107 1, 012411 (2023).

[9] Lorenzo Catani, Matthew Leifer, David Schmid, and Robert W. Spekkens, "Why interference phenomena do not capture the essence of quantum theory", Quantum 7, 1119 (2023).

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

[11] Ion Nechita, Clément Pellegrini, and Denis Rochette, "The asymmetric quantum cloning region", Letters in Mathematical Physics 113 3, 74 (2023).

[12] Kieran Flatt, Hanwool Lee, Carles Roch I Carceller, Jonatan Bohr Brask, and Joonwoo Bae, "Contextual Advantages and Certification for Maximum-Confidence Discrimination", PRX Quantum 3 3, 030337 (2022).

[13] David Schmid, Haoxing Du, John H. Selby, and Matthew F. Pusey, "Uniqueness of Noncontextual Models for Stabilizer Subtheories", Physical Review Letters 129 12, 120403 (2022).

[14] John H. Selby, David Schmid, Elie Wolfe, Ana Belén Sainz, Ravi Kunjwal, and Robert W. Spekkens, "Contextuality without Incompatibility", Physical Review Letters 130 23, 230201 (2023).

[15] John H. Selby, David Schmid, Elie Wolfe, Ana Belén Sainz, Ravi Kunjwal, and Robert W. Spekkens, "Accessible fragments of generalized probabilistic theories, cone equivalence, and applications to witnessing nonclassicality", Physical Review A 107 6, 062203 (2023).

[16] Rafael Wagner, Rui Soares Barbosa, and Ernesto F. Galvão, "Inequalities witnessing coherence, nonlocality, and contextuality", Physical Review A 109 3, 032220 (2024).

[17] David Schmid, John H. Selby, and Robert W. Spekkens, "Addressing some common objections to generalized noncontextuality", Physical Review A 109 2, 022228 (2024).

[18] John H. Selby, Elie Wolfe, David Schmid, Ana Belén Sainz, and Vinicius P. Rossi, "Linear Program for Testing Nonclassicality and an Open-Source Implementation", Physical Review Letters 132 5, 050202 (2024).

[19] Lorenzo Catani, Matthew Leifer, Giovanni Scala, David Schmid, and Robert W. Spekkens, "What is Nonclassical about Uncertainty Relations?", Physical Review Letters 129 24, 240401 (2022).

[20] Sumit Mukherjee, Shivam Naonit, and A. K. Pan, "Discriminating three mirror-symmetric states with a restricted contextual advantage", Physical Review A 106 1, 012216 (2022).

[21] Shiv Akshar Yadavalli and Ravi Kunjwal, "Contextuality in entanglement-assisted one-shot classical communication", Quantum 6, 839 (2022).

[22] Lorenzo Catani, Matthew Leifer, Giovanni Scala, David Schmid, and Robert W. Spekkens, "Aspects of the phenomenology of interference that are genuinely nonclassical", Physical Review A 108 2, 022207 (2023).

[23] Rafael Wagner, Anita Camillini, and Ernesto F. Galvão, "Coherence and contextuality in a Mach-Zehnder interferometer", Quantum 8, 1240 (2024).

[24] Costantino Budroni, Adán Cabello, Otfried Gühne, Matthias Kleinmann, and Jan-Åke Larsson, "Kochen-Specker contextuality", Reviews of Modern Physics 94 4, 045007 (2022).

[25] David Schmid, "A review and reformulation of macroscopic realism: resolving its deficiencies using the framework of generalized probabilistic theories", Quantum 8, 1217 (2024).

[26] Shihao Ru, Weidong Tang, Yunlong Wang, Feiran Wang, Pei Zhang, and Fuli Li, "Verification of Kochen-Specker-type quantum contextuality with a single photon", Physical Review A 105 1, 012428 (2022).

[27] Lorenzo Catani and Matthew Leifer, "A mathematical framework for operational fine tunings", Quantum 7, 948 (2023).

[28] Taira Giordani, Rafael Wagner, Chiara Esposito, Anita Camillini, Francesco Hoch, Gonzalo Carvacho, Ciro Pentangelo, Francesco Ceccarelli, Simone Piacentini, Andrea Crespi, Nicolò Spagnolo, Roberto Osellame, Ernesto F. Galvão, and Fabio Sciarrino, "Experimental certification of contextuality, coherence, and dimension in a programmable universal photonic processor", Science Advances 9 44, eadj4249 (2023).

[29] Chunwang Wu, Han Hu, Jie Zhang, Wenbo Su, Manchao Zhang, Tianxiang Zhan, Qingqing Qin, Wei Wu, and Pingxing Chen, "Experimental verification of quantum contextuality using a weak measurement in a single trapped ion", Physical Review A 109 3, 032211 (2024).

[30] Vinicius P. Rossi, David Schmid, John H. Selby, and Ana Belén Sainz, "Contextuality with vanishing coherence and maximal robustness to dephasing", Physical Review A 108 3, 032213 (2023).

[31] 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, (2019).

The above citations are from Crossref's cited-by service (last updated successfully 2024-05-21 07:05:43) and SAO/NASA ADS (last updated successfully 2024-05-21 07:05:44). The list may be incomplete as not all publishers provide suitable and complete citation data.