Understanding the interplay of entanglement and nonlocality: motivating and developing a new branch of entanglement theory

David Schmid1,2,3, Thomas C. Fraser1,2, Ravi Kunjwal4, Ana Belen Sainz3, Elie Wolfe1, and Robert W. Spekkens1

1Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario Canada N2L 2Y5
2Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
3International Centre for Theory of Quantum Technologies, University of Gdańsk, 80-308 Gdańsk, Poland
4Centre for Quantum Information and Communication, Ecole polytechnique de Bruxelles, CP 165, Université libre de Bruxelles, 1050 Brussels, Belgium

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Abstract

A standard approach to quantifying resources is to determine which operations on the resources are freely available, and to deduce the partial order over resources that is induced by the relation of convertibility under the free operations. If the resource of interest is the nonclassicality of the correlations embodied in a quantum state, i.e., $entanglement$, then the common assumption is that the appropriate choice of free operations is Local Operations and Classical Communication (LOCC). We here advocate for the study of a different choice of free operations, namely, Local Operations and Shared Randomness (LOSR), and demonstrate its utility in understanding the interplay between the entanglement of states and the nonlocality of the correlations in Bell experiments. Specifically, we show that the LOSR paradigm (i) provides a resolution of the $\textit{anomalies of nonlocality}$, wherein partially entangled states exhibit more nonlocality than maximally entangled states, (ii) entails new notions of genuine multipartite entanglement and nonlocality that are free of the pathological features of the conventional notions, and (iii) makes possible a resource-theoretic account of the self-testing of entangled states which generalizes and simplifies prior results. Along the way, we derive some fundamental results concerning the necessary and sufficient conditions for convertibility between pure entangled states under LOSR and highlight some of their consequences, such as the impossibility of catalysis for bipartite pure states. The resource-theoretic perspective also clarifies why it is neither surprising nor problematic that there are mixed entangled states which do not violate any Bell inequality. Our results motivate the study of LOSR-entanglement as a new branch of entanglement theory.

For the presentation “Why standard entanglement theory is inappropriate for the study of Bell scenarios” by David Schmid, please visit https://pirsa.org/20040095

We motivate and develop a new branch of entanglement theory, one where conversion relations between entangled states are evaluated relative to local operations and shared randomness rather than local operations and classical communication. We show that this notion of entanglement is particularly critical for studying the interplay of entanglement and nonlocality, offering a resolution of the long-standing `anomalies of nonlocality’, improving the definition of genuinely multipartite correlations, and yielding new opportunities for self-testing. The fact that classical communication plays no role in many prominent uses of entanglement theory suggests that the new notion will have many more applications.

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

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

[3] Patryk Lipka-Bartosik, Henrik Wilming, and Nelly H. Y. Ng, "Catalysis in Quantum Information Theory", arXiv:2306.00798, (2023).

[4] Martin Plávala, "General probabilistic theories: An introduction", Physics Reports 1033, 1 (2023).

[5] Miguel Navascués, Elie Wolfe, Denis Rosset, and Alejandro Pozas-Kerstjens, "Genuine Network Multipartite Entanglement", Physical Review Letters 125 24, 240505 (2020).

[6] Elie Wolfe, David Schmid, Ana Belén Sainz, Ravi Kunjwal, and Robert W. Spekkens, "Quantifying Bell: the Resource Theory of Nonclassicality of Common-Cause Boxes", Quantum 4, 280 (2020).

[7] Andrés F. Ducuara and Paul Skrzypczyk, "Operational Interpretation of Weight-Based Resource Quantifiers in Convex Quantum Resource Theories", Physical Review Letters 125 11, 110401 (2020).

[8] Elie Wolfe, Alejandro Pozas-Kerstjens, Matan Grinberg, Denis Rosset, Antonio Acín, and Miguel Navascués, "Quantum Inflation: A General Approach to Quantum Causal Compatibility", Physical Review X 11 2, 021043 (2021).

[9] Gilad Gour and Carlo Maria Scandolo, "Entanglement of a bipartite channel", arXiv:1907.02552, (2019).

[10] Gilad Gour and Carlo Maria Scandolo, "Dynamical Entanglement", Physical Review Letters 125 18, 180505 (2020).

[11] Joseph Schindler, Dominik Šafránek, and Anthony Aguirre, "Quantum correlation entropy", Physical Review A 102 5, 052407 (2020).

[12] Xavier Coiteux-Roy, Elie Wolfe, and Marc-Olivier Renou, "No Bipartite-Nonlocal Causal Theory Can Explain Nature's Correlations", Physical Review Letters 127 20, 200401 (2021).

[13] David Schmid, Denis Rosset, and Francesco Buscemi, "The type-independent resource theory of local operations and shared randomness", Quantum 4, 262 (2020).

[14] Denis Rosset, David Schmid, and Francesco Buscemi, "Type-Independent Characterization of Spacelike Separated Resources", Physical Review Letters 125 21, 210402 (2020).

[15] Eric Chitambar, Gilad Gour, Kuntal Sengupta, and Rana Zibakhsh, "Quantum Bell nonlocality as a form of entanglement", Physical Review A 104 5, 052208 (2021).

[16] Gilad Gour and Carlo Maria Scandolo, "Entanglement of a bipartite channel", Physical Review A 103 6, 062422 (2021).

[17] Tomáš Gonda and Robert W. Spekkens, "Monotones in General Resource Theories", arXiv:1912.07085, (2019).

[18] Ya-Li Mao, Zheng-Da Li, Sixia Yu, and Jingyun Fan, "Test of Genuine Multipartite Nonlocality", Physical Review Letters 129 15, 150401 (2022).

[19] Xavier Coiteux-Roy, Elie Wolfe, and Marc-Olivier Renou, "Any physical theory of nature must be boundlessly multipartite nonlocal", Physical Review A 104 5, 052207 (2021).

[20] Gilad Gour and Carlo Maria Scandolo, "Dynamical Resources", arXiv:2101.01552, (2020).

[21] Patryk Lipka-Bartosik and Paul Skrzypczyk, "All States are Universal Catalysts in Quantum Thermodynamics", Physical Review X 11 1, 011061 (2021).

[22] Elie Wolfe, Alejandro Pozas-Kerstjens, Matan Grinberg, Denis Rosset, Antonio Acín, and Miguel Navascues, "Quantum Inflation: A General Approach to Quantum Causal Compatibility", arXiv:1909.10519, (2019).

[23] Francesco Buscemi, Kodai Kobayashi, Shintaro Minagawa, Paolo Perinotti, and Alessandro Tosini, "Unifying different notions of quantum incompatibility into a strict hierarchy of resource theories of communication", Quantum 7, 1035 (2023).

[24] David Schmid, Haoxing Du, Maryam Mudassar, Ghi Coulter-de Wit, Denis Rosset, and Matty J. Hoban, "Postquantum common-cause channels: the resource theory of local operations and shared entanglement", Quantum 5, 419 (2021).

[25] Gennaro Zanfardino, Wojciech Roga, Masahiro Takeoka, and Fabrizio Illuminati, "Quantum resource theory of Bell nonlocality in Hilbert space", arXiv:2311.01941, (2023).

[26] Valentin Gebhart, Luca Pezzè, and Augusto Smerzi, "Genuine Multipartite Nonlocality with Causal-Diagram Postselection", Physical Review Letters 127 14, 140401 (2021).

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

[28] Matthew Girling, Cristina Cîrstoiu, and David Jennings, "Estimation of correlations and nonseparability in quantum channels via unitarity benchmarking", Physical Review Research 4 2, 023041 (2022).

[29] Peter Bierhorst, "Ruling out bipartite nonsignaling nonlocal models for tripartite correlations", Physical Review A 104 1, 012210 (2021).

[30] Martti Karvonen, "Neither Contextuality nor Nonlocality Admits Catalysts", Physical Review Letters 127 16, 160402 (2021).

[31] Shiv Akshar Yadavalli and Ravi Kunjwal, "Contextuality in entanglement-assisted one-shot classical communication", arXiv:2006.00469, (2020).

[32] Matthias Christandl, Nicholas Gauguin Houghton-Larsen, and Laura Mancinska, "An Operational Environment for Quantum Self-Testing", Quantum 6, 699 (2022).

[33] Tomáš Gonda, "Resource Theories as Quantale Modules", arXiv:2112.02349, (2021).

[34] Beata Zjawin, David Schmid, Matty J. Hoban, and Ana Belén Sainz, "The resource theory of nonclassicality of channel assemblages", Quantum 7, 1134 (2023).

[35] Kun Zhang and Jin Wang, "Entanglement versus Bell nonlocality of quantum nonequilibrium steady states", Quantum Information Processing 20 4, 147 (2021).

[36] Liang Huang, Xue-Mei Gu, Yang-Fan Jiang, Dian Wu, Bing Bai, Ming-Cheng Chen, Qi-Chao Sun, Jun Zhang, Sixia Yu, Qiang Zhang, Chao-Yang Lu, and Jian-Wei Pan, "Experimental Demonstration of Genuine Tripartite Nonlocality under Strict Locality Conditions", Physical Review Letters 129 6, 060401 (2022).

[37] Valentin Gebhart and Augusto Smerzi, "Extending the fair sampling assumption using causal diagrams", Quantum 7, 897 (2023).

[38] Kun Zhang and Jin Wang, "Asymmetric steerability of quantum equilibrium and nonequilibrium steady states through entanglement detection", Physical Review A 104 4, 042404 (2021).

[39] Peter Bierhorst and Jitendra Prakash, "Hierarchy of Multipartite Nonlocality and Device-Independent Effect Witnesses", Physical Review Letters 130 25, 250201 (2023).

[40] Patryk Lipka-Bartosik, Andrés Ducuara, Tom Purves, and Paul Skrzypczyk, "The operational significance of the quantum resource theory of Buscemi nonlocality", arXiv:2010.04585, (2020).

[41] Ravi Kunjwal and Ognyan Oreshkov, "Nonclassicality in correlations without causal order", arXiv:2307.02565, (2023).

[42] Qing Zhou, Xin-Yu Xu, Shu-Ming Hu, Shuai Zhao, Si-Xia Yu, Li Li, Nai-Le Liu, and Kai Chen, "Certifying genuine multipartite nonlocality without inequality in quantum networks", Physical Review A 107 5, 052416 (2023).

[43] Matty J. Hoban, Tom Drescher, and Ana Belén Sainz, "A hierarchy of semidefinite programs for generalised Einstein-Podolsky-Rosen scenarios", arXiv:2208.09236, (2022).

[44] Sansit Patnaik, Mehdi Jokar, Wei Ding, and Fabio Semperlotti, "Distillation of non-locality in\xA0porous solids", Proceedings of the Royal Society of London Series A 479 2275, 20220770 (2023).

The above citations are from Crossref's cited-by service (last updated successfully 2024-02-26 12:19:14) and SAO/NASA ADS (last updated successfully 2024-02-26 12:19:15). The list may be incomplete as not all publishers provide suitable and complete citation data.