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

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 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.

References in corpus (25)

• Device-independent security of quantum cryptography against collective attacks
• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Beyond Bell's Theorem: Correlation Scenarios
• Multipartite entanglement in spin chains
• Robust Self Testing of the Singlet
• Sum-of-squares decompositions for a family of CHSH-like inequalities and their application to self-testing
• Disproving the Peres conjecture: Bell nonlocality from bipartite bound entanglement
• Theory-independent limits on correlations from generalised Bayesian networks
• Secrecy extraction from no-signalling correlations
• Genuine Network Multipartite Entanglement
• Semi-device-independent bounds on entanglement
• Genuine multipartite nonlocality is intrinsic to quantum networks
• Quantum Inflation: A General Approach to Quantum Causal Compatibility
• The type-independent resource theory of local operations and shared randomness
• Quantum entanglement in the triangle network
• Type-independent Characterization of Spacelike Separated Resources
• Device-Independent Certification of Genuinely Entangled Subspaces
• Simulation of partial entanglement with nonsignaling resources
• A weak form of self-testing
• Postquantum common-cause channels: the resource theory of local operations and shared entanglement
• Quantifying EPR: the resource theory of nonclassicality of common-cause assemblages
• Monotones in General Resource Theories
• The resource theory of nonclassicality of channel assemblages
• Quantum Bell Nonlocality is Entanglement
• Recasting Mermin's multi-player game into the framework of pseudo-telepathy

Cited by in corpus (14)

• Genuine multipartite nonlocality with causal-diagram postselection
• Experimental demonstration of genuine tripartite nonlocality under strict locality conditions
• A review and reformulation of macroscopic realism: resolving its deficiencies using the framework of generalized probabilistic theories
• When is a Genuine Multipartite Entanglement Measure Monogamous?
• Every non-signalling channel is common-cause realizable
• Variations on the Choi-Jamiolkowski isomorphism
• Geometric measures of quantum nonlocality: characterization, quantification, and comparison by distances and operations
• Security of Device-independent Quantum Key Distribution under Sequential Attack
• The genuinely multipartite nonlocality of graph states is model-dependent
• Strength of statistical evidence for genuine tripartite nonlocality
• A hierarchy of semidefinite programs for generalised Einstein-Podolsky-Rosen scenarios
• Fully quantum inflation: quantum marginal problem constraints in the service of causal inference
• Analogs of absolutely maximally entangled states in nonlocal correlations via the sheaf-theoretic framework and its applications
• Localization of joint quantum measurements on ${\mathbb{C}}^d\otimes {\mathbb{C}}^d$ by entangled resources with Schmidt number at most $d$