A formalism for steering with local quantum measurements

Abstract

We develop a unified approach to classical, quantum and post-quantum steering. The framework is based on uncharacterised (black-box) parties performing quantum measurements on their share of a (possibly unphysical) quantum state, and its starting point is the characterisation of general no-signalling assemblages via non-positive local hidden-state models. By developing a connection to entanglement witnesses, this formalism allows for new definitions of families of assemblages, in particular via (i) non-decomposable positive maps and (ii) unextendible product bases. The former proves to be useful for constructing post-quantum assemblages with the built-in feature of yielding only quantum correlations in Bell experiments, while the latter always gives certifiably post-quantum assemblages. Finally, our framework is equipped with an inherent quantifier of post-quantum steering, which we call the negativity of post-quantum steering. We postulate that post-quantum steering should not increase under one-way quantum operations from the steered parties to the steering parties, and we show that, in this sense, the negativity of post-quantum steering is a convex post-quantum-steering monotone.

27 pages, 3 figures, one table. See related work by Matty J. Hoban and Ana Belén Sainz, arxiv:1708.xxxxx. Comments welcome

References in corpus (10)

• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements
• Multipartite entanglement in spin chains
• Joint measurability of generalized measurements implies classicality
• Almost quantum correlations
• Optimal entanglement criterion for mixed quantum states
• All entangled states are useful for channel discrimination
• Implausible Consequences of Superstrong Nonlocality
• A channel-based framework for steering, non-locality and beyond
• Nonlocality free wirings and the distinguishability between Bell boxes

Cited by in corpus (15)

• Quantum Steering
• Semi-definite programming and quantum information
• Postquantum common-cause channels: the resource theory of local operations and shared entanglement
• Bipartite post-quantum steering in generalised scenarios
• Post-quantum steering is a stronger-than-quantum resource for information processing
• Exploring the framework of assemblage moment matrices and its applications in device-independent characterizations
• On characterising assemblages in Einstein-Podolsky-Rosen scenarios
• Exposure of subtle multipartite quantum nonlocality
• On the edge of the set of no-signaling assemblages
• Activation of post-quantumness in bipartite generalised EPR scenarios
• Single trusted qubit is necessary and sufficient for quantum realisation of extremal no-signaling correlations
• Activation of post-quantum steering
• A hierarchy of semidefinite programs for generalised Einstein-Podolsky-Rosen scenarios
• Classical-to-quantum non-signalling boxes
• Hybrid no-signaling-quantum correlations