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Journal of Quantum Information Science

A Sufficient Clarification of “Super-Quantum Correlations: A Necessary Clarification” by Pierre Uzan

Nicolas Courtemanche, Claude Crépeau

Published Jan 1, 2021• 2 citations
Publisher

Abstract

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.

DOI
10.4236/jqis.2021.112005

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•Jan 1, 2015•2 citations
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.
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.
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.
The phenomenon of nonlocality, which can arise when entangled quantum systems are suitably measured, is perhaps one of the most puzzling features of quantum theory to the philosophical mind. It implies that these measurement statistics cannot be explained by hidden variables, as requested by Einstein, and it thus suggests that our universe may not be, in principle, a well-determined entity where the uncertainty we perceive in physical observations stems only from our lack of knowledge of the whole. Besides its philosophical impact, nonlocality is also a resource for information- theoretic tasks since it implies secrecy: If nonlocality limits the predictive power that any hidden variable (in the universe) can have about some observations, then it limits in particular the predictive power of a hidden variable held by an adversary in a cryptographic scenario. We investigate whether nonlocality alone can empower two parties to perform unconditionally secure communication in a feasible manner when only a provably minimal set of assumptions are made for such a task to be possible — independently of the validity of any physical theory (such as quantum theory). Nonlocality has also been of interest in the study of foundations of quantum theory and the principles that stand beyond its mathematical formalism. In an attempt to single out quantum theory within a broader set of theories, the study of nonlocality may help to point out intuitive principles that distinguish it from the rest. In theories where the limits by which quantum theory constrains the strength of nonlocality are surpassed, many “principles” on which an information theorist would rely on are shattered — one example is the hierarchy of communication complexity as the latter becomes completely trivial once a certain degree of nonlocality is overstepped. In order to study the structure of such super-quantum theories — beyond their aforementioned secrecy aspects — we investigate the phenomenon of distillation of nonlocality, the ability to distill stronger forms of nonlocality from weaker ones. By exploiting the inherent connection between nonlocality and secrecy, we provide a novel way of deriving bounds on nonlocality-distillation protocols through an ad versarial view to the problem.