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Journal of Quantum Information Science

Super-Quantum Correlations: A Necessary Clarification

Pierre Uzan

Published Jan 1, 2018• 2 citations
Publisher

Abstract

This paper proposes a necessary clarification about the problematic of super-quantum correlations, whose mainstream debate relies on an incorrect, statistical interpretation of the no-signaling condition. The no-signaling condition is an informational constraint that limits the strength of non-local correlations to the Tsirelson bound.
DOI
10.4236/jqis.2018.83009

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This article deals with the question of the maximal correlation degree of two intelligent machines that cannot exchange any signals. After reminding the reader of the incorrectness of the mainstream statistical interpretation of the “no-signaling” condition, its informational meaning is explored. It is emphasized that if Pawlowski et al.’s Information Causality Principle correctly expresses (and generalizes) the no-signaling condition, its application is, for now, based on a specific scenario (suggested by van Dam) and a no less specific (and simplified) relationship between mutual information and correlators. A more general informational interpretation of the no-signaling condition from which the Tsirelson bound can be derived is then formulated in terms of correlational independence.
This article shows that the mainstream discussion about super-quantum correlations is skewed by an incorrect interpretation of the “no-signaling” condition (NS). Referring to counter-examples, it shows that the usual probabilistic interpretation of (NS), whose link with relativistic causality is doubtful, is too weak to assert the absence of any exchange of information between the parties. A relevant informal interpretation of (NS) is nothing but a particular specification of Pawlowski’s Information Causality principle, which rules out the possibility of correlations stronger than the strongest quantum correlations.
In the paper “Super-Quantum Correlations: A Necessary Clarification” by Uzan [1], it is suggested that stronger than quantum (or supra-quantum) correlations are not possible. The main point of Uzan’s argumentation is the belief that the intuitive definition of No-Signalling (NS) is different from the statistical definition of No-Signalling (NSstat), and that situations exist where NSstat is respected while NS isn’t. In this paper we show why these definitions are one and the same, and where the example from the original paper breaks down. We provide a broader context to help the reader understand intuitively the situation.
The idea that nonlocal correlations stronger than quantum correlations between two no-signaling systems could “theoretically” exist is based on an incorrect statistical interpretation of the no-signaling condition. This article shows that any physically realizable no-signaling “box” involving local incompatible observables indeed requires to be described in a noncommutative, quantum-like language of operators, which leads to the derivation of the Tsirelson bound and then contradicts this idea.