Graph Structured Operator Inequalities and Tsirelson-Type Bounds

TL;DR

This paper develops new operator norm inequalities for bipartite tensor sums, generalizing Tsirelson bounds and linking them to quantum information concepts like Bell correlations and network nonlocality.

Contribution

It introduces a graph-based framework for operator inequalities that captures sparse interactions and provides dimension-free estimates relevant to quantum information theory.

Findings

Derived dimension-free operator norm bounds for bipartite tensor sums.

Connected operator inequalities to quantum nonlocality and Bell correlations.

Provided closed-form estimates complementing existing numerical methods.

Abstract

We establish operator norm bounds for bipartite tensor sums of self-adjoint contractions. The inequalities generalize the analytic structure underlying the Tsirelson and CHSH bounds, giving dimension-free estimates expressed through commutator and anticommutator norms. A graph based formulation captures sparse interaction patterns via constants depending only on graph connectivity. The results link analytic operator inequalities with quantum information settings such as Bell correlations and network nonlocality, offering closed-form estimates that complement semidefinite and numerical methods.