A formalism for steering with local quantum measurements

A B Sainz, L Aolita, M Piani, M J Hoban, P Skrzypczyk

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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.
Original languageEnglish
Article number083040
Number of pages17
JournalNew Journal of Physics
Volume20
DOIs
Publication statusPublished - 28 Aug 2018

Keywords

  • quantum measurements
  • quantum state
  • non-decomposable positive maps
  • unextendible product bases
  • steering

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Cite this

Sainz, A. B., Aolita, L., Piani, M., Hoban, M. J., & Skrzypczyk, P. (2018). A formalism for steering with local quantum measurements. New Journal of Physics, 20, [083040]. https://doi.org/10.1088/1367-2630/aad8df