A formalism for steering with local quantum measurements

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Sainz, Ana Belén; Aolita, Leandro; Piani, Marco; Hoban, Matty J. and Skrzypczyk, Paul. 2018. A formalism for steering with local quantum measurements. New Journal of Physics, 20, 083040. ISSN 1367-2630 [Article]

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Official URL: http://iopscience.iop.org/article/10.1088/1367-263...

Abstract or Description

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.

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Article

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https://doi.org/10.1088/1367-2630/aad8df