The resource theory of nonclassicality of channel assemblages

Abstract

When two parties, Alice and Bob, share correlated quantum systems and Alice performs local measurements, Alice's updated description of Bob's state can provide evidence of nonclassical correlations. This simple scenario, famously introduced by Einstein, Podolsky and Rosen (EPR), can be modified by allowing Bob to also have a classical or quantum system as an input. In this case, Alice updates her knowledge of the channel (rather than of a state) in Bob's lab. In this paper, we provide a unified framework for studying the nonclassicality of various such generalizations of the EPR scenario. We do so using a resource theory wherein the free operations are local operations and shared randomness (LOSR). We derive a semidefinite program for studying the pre-order of EPR resources and discover possible conversions between the latter. Moreover, we study conversions between post-quantum resources both analytically and numerically.

V2 changes: Accepted by Quantum, bibliography hyperlinks adjusted according to journal policy, small changes in text

References in corpus (9)

• Steering, Entanglement, Nonlocality, and the EPR Paradox
• A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
• Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox
• Bounding the set of quantum correlations
• Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements
• Almost quantum correlations
• Non-locality distillation and post-quantum theories with trivial communication complexity
• Channel Steering
• Quantifying EPR: the resource theory of nonclassicality of common-cause assemblages

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• Every non-signalling channel is common-cause realizable
• Certifying nonlocal properties of noisy quantum operations
• Activation of post-quantumness in bipartite generalised EPR scenarios
• Activation of post-quantum steering
• Classical-to-quantum non-signalling boxes