A channel-based framework for steering, non-locality and beyond

Abstract

Non-locality and steering are both non-classical phenomena witnessed in Nature as a result of quantum entanglement. It is now well-established that one can study non-locality independently of the formalism of quantum mechanics, in the so-called device-independent framework. With regards to steering, although one cannot study it completely independently of the quantum formalism, "post-quantum steering" has been described, which is steering that cannot be reproduced by measurements on entangled states, but do not lead to superluminal signalling. In this work we present a framework based on the study of quantum channels in which one can study steering (and non-locality) in quantum theory and beyond. In this framework, we show that kinds of steering, whether quantum or post-quantum, are directly related to particular families of quantum channels that have been previously introduced by Beckman, Gottesman, Nielsen, and Preskill [Phys. Rev. A 64, 052309 (2001)]. Utilising this connection we also demonstrate new analytical examples of post-quantum steering, give a quantum channel interpretation of almost quantum non-locality and steering, easily recover and generalise the celebrated Gisin-Hughston-Jozsa-Wootters theorem, and initiate the study of post-quantum Buscemi non-locality and non-classical teleportation. In this way, we see post-quantum non-locality and steering as just two aspects of a more general phenomenon.

Updated with corrections of typos and significant restructuring. 55 pages, 17 figures. See related work by A. B. Sainz, L. Aolita, M. Piani, M. J. Hoban and P. Skrzypczyk, arxiv:1708.00756. Comments welcome

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• Device-independent security of quantum cryptography against collective attacks
• Steering, Entanglement, Nonlocality, and the EPR Paradox
• A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
• Private Randomness Expansion With Untrusted Devices
• Joint measurability of generalized measurements implies classicality
• Almost quantum correlations
• Connes' embedding problem and Tsirelson's problem
• Measurement-Device-Independent Entanglement Witnesses for All Entangled Quantum States
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Cited by in corpus (33)

• Quantum Steering
• The type-independent resource theory of local operations and shared randomness
• Type-independent Characterization of Spacelike Separated Resources
• Incompatible measurements in a class of general probabilistic theories
• Quantum Channel Marginal Problem
• Understanding the interplay of entanglement and nonlocality: motivating and developing a new branch of entanglement theory
• Semi-definite programming and quantum information
• Postquantum common-cause channels: the resource theory of local operations and shared entanglement
• Estimating entanglement in teleportation experiments
• A formalism for steering with local quantum measurements
• Bipartite post-quantum steering in generalised scenarios
• Quantifying EPR: the resource theory of nonclassicality of common-cause assemblages
• Post-quantum steering is a stronger-than-quantum resource for information processing
• Self-testing and certification using trusted quantum inputs
• Necessary and Sufficient Conditions on Measurements of Quantum Channels
• The resource theory of nonclassicality of channel assemblages
• Semi-Device-Independent Certification of Causal Nonseparability with Trusted Quantum Inputs
• Incompatibility in restricted operational theories: connecting contextuality and steering
• Popescu-Rohrlich box implementation in general probabilistic theory of processes
• Operational Interpretation of the Choi Rank Through k-State Exclusion
• On characterising assemblages in Einstein-Podolsky-Rosen scenarios
• Network-Device-Independent Certification of Causal Nonseparability
• Every non-signalling channel is common-cause realizable
• Unified Approach to Witness Nonentanglement-Breaking Quantum Channels
• On the edge of the set of no-signaling assemblages
• Certifying nonlocal properties of noisy quantum operations
• Structure of quantum and classical implementations of Popescu-Rohrlich box
• Symmetries and Wigner representations of operational theories
• Activation of post-quantum steering
• Hybrid no-signaling-quantum correlations
• A hierarchy of semidefinite programs for generalised Einstein-Podolsky-Rosen scenarios
• Detection of the genuine non-locality of any three-qubit state
• Classical-to-quantum non-signalling boxes