A formalism for steering with local quantum measurements. (28th August 2018)

• Record Type: Journal Article
• Authors: Sainz, A B; Aolita, L; Piani, M; Hoban, M J; Skrzypczyk, P
• Is Part Of: New journal of physics. Volume 20:Number 8(2018:Aug.)
• Publication Date: 2018-08-28
• Subjects: quantum non-locality -- EPR steering -- quantum maps -- entanglement witnesses; Physics -- Periodicals; Physics; Periodicals; 530.05
• DOI: 10.1088/1367-2630/aad8df
• Languages: English
• ISSNs: 1367-2630

Abstract

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, which will be defined in this work. 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.