Quantifying non-classical and beyond-quantum correlations in the unified operator formalism

Joshua Geller, Marco Piani

Research output: Contribution to journalSpecial issue

9 Citations (Scopus)
83 Downloads (Pure)

Abstract

Acin et al (2010 Phys. Rev. Lett. 104 140404) introduced a unified framework for the study of no-signalling correlations. Such a framework is based on the notion of local quantum measurements, but, in order to account for beyond quantum correlations, global pseudo-states that are not positive semidefinite are allowed. After a short review of the formalism, we consider its use in the quantification of both general non-local and beyond-quantum correlations. We argue that the unified framework for correlations provides a simple approach to such a quantification, in particular when the quantification is meant to be operational and meaningful in a resource-theory scenario, i.e., when considering the processing of resources by means of non-resources. We relate different notions of robustness of correlations, both at the level of (pseudo-)states and abstract probability distributions, with particular focus on the beyond-quantum robustness of correlations and pseudo-states. We revisit known results and argue that, within the unified framework, the relation between the two levels—that of operators and that of probability distributions—is very strict. We point out how the consideration of robustness at the two levels leads to a natural framework for the quantification of entanglement in a device independent way. Finally, we show that the beyond-quantum robustness of the non-positive operators needed to achieve beyond-quantum correlations coincides with their negativity and their distance from the set of quantum states. As an example, we calculate the beyond-quantum robustness for the case of a noisy Popescu–Rohrlich box.
Original languageEnglish
Article number424030
Number of pages18
JournalJournal of Physics A: Mathematical and Theoretical
Volume47
Issue number42
DOIs
Publication statusPublished - 8 Oct 2014

Keywords

  • quantum nonlocality
  • robustness of correlations
  • entanglement
  • Popescu–Rohrlich box
  • pseudo-state
  • device-independent

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