de Finetti reductions for correlations

Rotem Arnon-Friedman, Renato Renner

Research output: Contribution to journalArticlepeer-review

Abstract

When analysing quantum information processing protocols, one has to deal with large entangled systems, each consisting of many subsystems. To make this analysis feasible, it is often necessary to identify some additional structures. de Finetti theorems provide such a structure for the case where certain symmetries hold. More precisely, they relate states that are invariant under permutations of subsystems to states in which the subsystems are independent of each other. This relation plays an important role in various areas, e.g., in quantum cryptography or state tomography, where permutation invariant systems are ubiquitous. The known de Finetti theorems usually refer to the internal quantum state of a system and depend on its dimension. Here, we prove a different de Finetti theorem where systems are modelled in terms of their statistics under measurements. This is necessary for a large class of applications widely considered today, such as device independent protocols, where the underlying systems and the dimensions are unknown and the entire analysis is based on the observed correlations. (C) 2015 Author(s).

Original languageEnglish
Article number052203
Number of pages23
JournalJournal of Mathematical Physics
Volume56
Issue number5
DOIs
StatePublished - May 2015
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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