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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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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The above citations are from Crossref's cited-by service (last updated successfully 2024-06-22 04:44:38) and SAO/NASA ADS (last updated successfully 2024-06-22 04:44:39). The list may be incomplete as not all publishers provide suitable and complete citation data.