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The Debate on Super-quantum Correlations: Statistical Misinterpretation and Logical Fallacy

Pierre Uzan

Published Mar 4, 2022• 0 citations
Publisher

Abstract

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.

DOI
10.9734/bpi/rtcps/v7/2719c

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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.
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.
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Understanding the concept of causality is fundamental in physics, as it conditions the very possibility of any exchange of information between physical systems. This article examines and compares three main interpretations of the correlative operational concept of "causal separation" that have been respectively proposed in special relativity, quantum theory, and according to the statistical "non-signalling" condition. These interpretations, which can be classified regarding the range of CHSH correlation degrees they allow, lead to radically different results regarding the exchange of information between physical systems. Namely, it can be shown that, in opposition with the non-communication theorem of quantum theory, non-local communication can be established between the two entangled parts of a physical system when the relativistic criterium of causal separation is satisfied but not the quantum one.