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Why the Tsirelson Bound?

Jeffrey Bub

Published Aug 16, 2016• 12 citations
OpenAlex

Abstract

Wheeler's question 'why the quantum' has two aspects: why is the world quantum and not classical, and why is it quantum rather than superquantum, i.e., why the Tsirelson bound for quantum correlations? I discuss a remarkable answer to this question proposed by Pawłowski et al. [1], who provide an information-theoretic derivation of the Tsirelson bound from a principle they call 'information causality.'

Related papers

Why the Quantum?

Jeffrey Bub

What principle excludes superquantum correlations that don’t violate the nosignaling principle? In an argument using PR boxes in a 2009 Nature paper, Pawlowski and colleagues show that the Tsirelson bound – the limit achievable in a simulation of a Popescu–Rohrlich correlation with quantum resources – follows from an information-theoretic principle they call “information causality.” For three qubits, it is now known that there are superquantum correlations that cannot be excluded by a bipartite principle like information causality, so this principle does not completely characterize quantum correlations. An intriguing principle, developed by Cabello as the “exclusivity principle” or “Specker’s principle” (from Ernst Specker’s story about a seer from Nineva), and separately by Fritz and colleagues as the principle of “local orthogonality,” yields the Tsirelson bound, and also rules out correlations beyond the quantum limit for the Klyachko correlation and other cases where contextuality or nonlocality is relevant.

Oxford University Press eBooks•Feb 11, 2016•0 citations

Stronger-than-quantum bipartite correlations violate relativistic causality in the classical limit

Daniel Rohrlich

Superquantum ("PR-box") correlations, though designed to respect relativistic causality, violate relativistic causality in the classical limit. Generalizing to all stronger-than-quantum bipartite correlations, I derive Tsirelson's bound from the axioms of nonlocality, relativistic causality and the existence of a classical limit. This derivation of Tsirelson's bound does not assume quantum mechanics yet suggests how Hilbert space is implicit in quantum correlations.

arXiv:1408.3125•Aug 13, 2014•4 citations

Bounding Quantum Correlations: The Role of the Shannon Information in the Information Causality Principle

Natasha Oughton, Christopher G. Timpson

The Information Causality principle was proposed to re-derive the Tsirelson bound, an upper limit on the strength of quantum correlations, and has been suggested as a candidate law of nature. The principle states that the Shannon information about Alice’s distant database gained by Bob after receiving an m bit message cannot exceed m bits, even when Alice and Bob share non-local resources. As originally formulated, it can be shown that the principle is violated exactly when the strength of the shared correlations exceeds the Tsirelson bound. However, we demonstrate here that when an alternative measure of information, one of the Renyi measures, is chosen, the Information Causality principle no longer arrives at the correct value for the Tsirelson bound. We argue that neither the assumption of particular ‘intuitive’ properties of uncertainties measures, nor pragmatic choices about how to optimise costs associated with communication, are sufficient to motivate uniquely the choice of the Shannon measure from amongst the more general Renyi measures. We conclude that the dependence of the success of Information Causality on mere convention undermines its claimed significance as a foundational principle.

Entropy•Jun 29, 2024•2 citations

Information Causality, the Tsirelson Bound, and the 'Being-Thus' of Things

Michael E. Cuffaro

The principle of `information causality' can be used to derive an upper bound---known as the `Tsirelson bound'---on the strength of quantum mechanical correlations, and has been conjectured to be a foundational principle of nature. To date, however, it has not been sufficiently motivated to play such a foundational role. The motivations that have so far been given are, as I argue, either unsatisfactorily vague or appeal to little if anything more than intuition. Thus in this paper I consider whether some way might be found to successfully motivate the principle. And I propose that a compelling way of so doing is to understand it as a generalisation of Einstein's principle of the mutually independent existence---the `being-thus'---of spatially distant things. In particular I first describe an argument, due to Demopoulos, to the effect that the so-called `no-signalling' condition can be viewed as a generalisation of Einstein's principle that is appropriate for an irreducibly statistical theory such as quantum mechanics. I then argue that a compelling way to motivate information causality is to in turn consider it as a further generalisation of the Einsteinian principle that is appropriate for a theory of communication. I describe, however, some important conceptual obstacles that must yet be overcome if the project of establishing information causality as a foundational principle of nature is to succeed.

•Aug 29, 2017•5 citations

Super-Quantum Correlations: How to Interpret the No-Signaling Condition?

Pierre Uzan

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.

Transactions on Machine Learning and Artificial Intelligence•Jul 7, 2022•0 citations

Indistinguishability as nonlocality constraint

Cássio Sozinho Amorim

A physical explanation for quantum bounds to nonlocality (Tsirelson's bound) is a fundamental problem in quantum theory, for it is known that no-signaling alone fails to reproduce this limit. Here, information indistinguishability is presented as the indistinguishability of qubits or more general bits, and it suggests an answer to the nonlocality conundrum, ultimately placing it as the origin to quantum limits. Indistinguishability is also connected to exclusivity principle, and it is shown that indistinguishability leads to quantum correlation bounds. This suggests indistinguishability be as fundamental as non-locality and relativistic causality for nonlocal realism.

arXiv:1610.03605•Scientific Reports•Apr 11, 2018•4 citations
Wheeler's question 'why the quantum' has two aspects: why is the world quantum and not classical, and why is it quantum rather than superquantum, i.e., why the Tsirelson bound for quantum correlations? I discuss a remarkable answer to this question proposed by Pawłowski et al. [1], who provide an information-theoretic derivation of the Tsirelson bound from a principle they call 'information causality.'
What principle excludes superquantum correlations that don’t violate the nosignaling principle? In an argument using PR boxes in a 2009 Nature paper, Pawlowski and colleagues show that the Tsirelson bound – the limit achievable in a simulation of a Popescu–Rohrlich correlation with quantum resources – follows from an information-theoretic principle they call “information causality.” For three qubits, it is now known that there are superquantum correlations that cannot be excluded by a bipartite principle like information causality, so this principle does not completely characterize quantum correlations. An intriguing principle, developed by Cabello as the “exclusivity principle” or “Specker’s principle” (from Ernst Specker’s story about a seer from Nineva), and separately by Fritz and colleagues as the principle of “local orthogonality,” yields the Tsirelson bound, and also rules out correlations beyond the quantum limit for the Klyachko correlation and other cases where contextuality or nonlocality is relevant.
The Information Causality principle was proposed to re-derive the Tsirelson bound, an upper limit on the strength of quantum correlations, and has been suggested as a candidate law of nature. The principle states that the Shannon information about Alice’s distant database gained by Bob after receiving an m bit message cannot exceed m bits, even when Alice and Bob share non-local resources. As originally formulated, it can be shown that the principle is violated exactly when the strength of the shared correlations exceeds the Tsirelson bound. However, we demonstrate here that when an alternative measure of information, one of the Renyi measures, is chosen, the Information Causality principle no longer arrives at the correct value for the Tsirelson bound. We argue that neither the assumption of particular ‘intuitive’ properties of uncertainties measures, nor pragmatic choices about how to optimise costs associated with communication, are sufficient to motivate uniquely the choice of the Shannon measure from amongst the more general Renyi measures. We conclude that the dependence of the success of Information Causality on mere convention undermines its claimed significance as a foundational principle.
The principle of `information causality' can be used to derive an upper bound---known as the `Tsirelson bound'---on the strength of quantum mechanical correlations, and has been conjectured to be a foundational principle of nature. To date, however, it has not been sufficiently motivated to play such a foundational role. The motivations that have so far been given are, as I argue, either unsatisfactorily vague or appeal to little if anything more than intuition. Thus in this paper I consider whether some way might be found to successfully motivate the principle. And I propose that a compelling way of so doing is to understand it as a generalisation of Einstein's principle of the mutually independent existence---the `being-thus'---of spatially distant things. In particular I first describe an argument, due to Demopoulos, to the effect that the so-called `no-signalling' condition can be viewed as a generalisation of Einstein's principle that is appropriate for an irreducibly statistical theory such as quantum mechanics. I then argue that a compelling way to motivate information causality is to in turn consider it as a further generalisation of the Einsteinian principle that is appropriate for a theory of communication. I describe, however, some important conceptual obstacles that must yet be overcome if the project of establishing information causality as a foundational principle of nature is to succeed.
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.
A physical explanation for quantum bounds to nonlocality (Tsirelson's bound) is a fundamental problem in quantum theory, for it is known that no-signaling alone fails to reproduce this limit. Here, information indistinguishability is presented as the indistinguishability of qubits or more general bits, and it suggests an answer to the nonlocality conundrum, ultimately placing it as the origin to quantum limits. Indistinguishability is also connected to exclusivity principle, and it is shown that indistinguishability leads to quantum correlation bounds. This suggests indistinguishability be as fundamental as non-locality and relativistic causality for nonlocal realism.