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Physics Essays

Why superquantum, no-signaling correlations cannot exist

Pierre Uzan

Published Jun 15, 2020• 1 citation
Publisher

Abstract

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.

DOI
10.4006/0836-1398-33.2.140

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•Jan 1, 2019•7 citations
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.
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.
Abstract Bell’s theorem renders quantum correlations distinct from those of any local-realistic model. Although being stronger than classical correlations, quantum correlations are limited by the Tsirelson bound. This bound, however, applies for Hermitian, commutative operators corresponding to non-signaling observables in Alice’s and Bob’s spacelike-separated labs. As an attempt to explore theories beyond quantum mechanics and analyze the uniqueness of the latter, we examine in this work the extent of non-local correlations when relaxing these fundamental assumptions, which allows for theories with non-local signaling. We prove that, somewhat surprisingly, the Tsirelson bound in the Bell–Clauser–Horne–Shimony–Holt scenario, and similarly other related bounds on non-local correlations, remain effective as long as we maintain the Hilbert space structure of the theory. Furthermore, in the case of Hermitian observables we find novel relations between non-locality, local correlations, and signaling. We demonstrate that such non-local signaling theories are naturally simulated by quantum systems of parafermionic zero modes. We numerically study the derived bounds in parafermionic systems, confirming the bounds’ validity yet finding a drastic difference between correlations of ‘signaling’ and ‘non-signaling’ sets of observables. We also propose an experimental procedure for measuring the relevant correlations.
Bell's theorem renders quantum correlations distinct from those of any local-realistic model. Although being stronger than classical correlations, quantum correlations are limited by the Tsirelson bound. This bound, however, applies for Hermitian, commutative operators corresponding to non-signaling observables in Alice's and Bob's spacelike-separated labs. As an attempt to explore theories beyond quantum mechanics and analyze the uniqueness of the latter, we examine in this work the extent of non-local correlations when relaxing these fundamental assumptions, which allows for theories with non-local signaling. We prove that, somewhat surprisingly, the Tsirelson bound in the Bell-Clauser-Horne-Shimony-Holt scenario, and similarly other related bounds on non-local correlations, remain effective as long as we maintain the Hilbert space structure of the theory. Furthermore, in the case of Hermitian observables we find novel relations between non-locality, local correlations, and signaling. We demonstrate that such non-local signaling theories are naturally simulated by quantum systems of parafermionic zero modes. We numerically study the derived bounds in parafermionic systems, confirming the bounds' validity yet finding a drastic difference between correlations of 'signaling' and 'non-signaling' sets of observables. We also propose an experimental procedure for measuring the relevant correlations.