A formalism for steering with local quantum measurements

Ana Belen Sainz, L. Aolita, M. Piani, M. J. Hoban, P. Skrzypczyk

Research output: Contribution to journalArticle (Academic Journal)peer-review

5 Citations (Scopus)
283 Downloads (Pure)


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.

Original languageEnglish
Article number083040
Number of pages18
JournalNew Journal of Physics
Issue number8
Early online date28 Aug 2018
Publication statusPublished - Aug 2018

Structured keywords

  • Bristol Quantum Information Institute
  • QITG


  • entanglement witnesses
  • EPR steering
  • quantum maps
  • quantum non-locality

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