What question did this study set out to answer?

The aim is to demonstrate how information causality impacts the positive semi-definiteness of quantum correlation kernels.

March 27, 2026Open Access

Information Causality Implies Kernel Positivity and Geometric Robustness of Quantum Correlations

Key Points

The aim is to demonstrate how information causality impacts the positive semi-definiteness of quantum correlation kernels.
Applied information causality principle to enforce positive semi-definiteness.
Utilized Herglotz's theorem in the analysis.
Examined Tsirelson bound saturation for quantum correlations.
Extended findings to the hyperbolic plane H².
Established that positive semi-definiteness is enforced by information causality.
Demonstrated the strict bound of the CHSH value by 2√2 in hyperbolic geometry.
Concluded that Tsirelson bound represents a universal limit, not confined to Euclidean geometry.

Abstract

We demonstrate that the principle of Information Causality (IC) is sufficient to enforce the positive semi-definiteness (PSD) of bipartite correlation kernels. By combining this result with Herglotz's theorem and the requirement of Tsirelson bound saturation, we close the axiomatic gap in the derivation of the quantum correlation law E(Δθ) = −cos(Δθ). Furthermore, we extend this framework to the hyperbolic plane H². We show that despite the negative curvature, which allows for different positive-definite harmonic modes, the maximal CHSH value remains strictly bounded by 2√2. This reveals that the Tsirelson bound is not merely an artifact of flat Euclidean geometry, but a universal, geometrically robust limit enforced by Information Causality.

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