A formalism for steering with local quantum measurements

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

Research output: Contribution to journalArticle

2 Citations (Scopus)

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

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Keywords

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

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
Sainz, A B ; Aolita, L ; Piani, M ; Hoban, M J ; Skrzypczyk, P. / A formalism for steering with local quantum measurements. In: New Journal of Physics. 2018 ; Vol. 20.
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Sainz, AB, Aolita, L, Piani, M, Hoban, MJ & Skrzypczyk, P 2018, 'A formalism for steering with local quantum measurements' New Journal of Physics, vol. 20, 083040. https://doi.org/10.1088/1367-2630/aad8df

A formalism for steering with local quantum measurements. / Sainz, A B; Aolita, L; Piani, M; Hoban, M J; Skrzypczyk, P.

In: New Journal of Physics, Vol. 20, 083040, 28.08.2018.

Research output: Contribution to journalArticle

TY - JOUR

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AU - Sainz, A B

AU - Aolita, L

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PY - 2018/8/28

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N2 - 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.

AB - 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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Sainz AB, Aolita L, Piani M, Hoban MJ, Skrzypczyk P. A formalism for steering with local quantum measurements. New Journal of Physics. 2018 Aug 28;20. 083040. https://doi.org/10.1088/1367-2630/aad8df