Recovering part of the boundary between quantum and nonquantum correlations from information causality

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 80, Issue 4, 2009, Pages

  Allcock, Jonathan ^a   Brunner, Nicolas ^a   Pawlowski, Marcin ^b   Scarani, Valerio ^c  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

^b UNIVERSITY OF GDA SK   (Poland)

^c NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

QUANTUM CORRELATIONS;

INFORMATION THEORY;

EID: 70449345854     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.80.040103     Document Type: Article

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33. Tsirelson and Masanes proved that if a given set of correlators satisfies the TLM criterion, there exists a probability distribution admitting a quantum description that has this set of correlators. Here, the question is whether this quantum probability distribution could have the form of correlations in family 1. This is indeed the case since any probability distribution can be brought to a form where the marginals are unbiased and the joint probabilities satisfy P (a,b x,y) =P (a□1,b□1□x,y). Importantly, this can be done by local operations without modifying the value of the correlators; Alice and Bob share a random bit α and subsequently modify their output according to a→a□α and b→b□α. Thus, the TLM criterion is necessary and sufficient for quantumness in the slices of the polytope in family 1.