The chain rule implies Tsirelson's bound: an approach from generalized mutual information

Abstract

In order to analyze an information theoretical derivation of Tsirelson's bound based on information causality, we introduce a generalized mutual information (GMI), defined as the optimal coding rate of a channel with classical inputs and general probabilistic outputs. In the case where the outputs are quantum, the GMI coincides with the quantum mutual information. In general, the GMI does not necessarily satisfy the chain rule. We prove that Tsirelson's bound can be derived by imposing the chain rule on the GMI. We formulate a principle, which we call the no-supersignalling condition, which states that the assistance of nonlocal correlations does not increase the capability of classical communication. We prove that this condition is equivalent to the no-signalling condition. As a result, we show that Tsirelson's bound is implied by the nonpositivity of the quantitative difference between information causality and no-supersignalling.

23 pages, 8 figures, Added Section 2 and Appendix B, result unchanged, Added references

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Cited by in corpus (6)

• Dimension of physical systems, information processing, and thermodynamics
• Information-theoretic constraints on correlations with indefinite causal order
• Nonlinear Schrödinger equations and generalized Heisenberg uncertainty principle violating the principle of estimation independence
• Estimation independence as an axiom for quantum uncertainty
• Tests for quantum contextuality in terms of $q$-entropies
• Quantum correlations and causal structures