Monogamy Relation in No-disturbance Theories

TL;DR

This paper explores the monogamy relations in no-disturbance theories, establishing conditions and tradeoff relations for Bell and noncontextual inequalities in multi-party quantum systems.

Contribution

It provides new sufficient conditions for the validity of cycle noncontextual and CHSH inequalities and derives various monogamy tradeoff relations in no-disturbance frameworks.

Findings

Established conditions for noncontextual inequalities to hold.

Derived tradeoff relations for monogamy of Bell and noncontextual inequalities.

Discussed generalized CHSH inequalities in multi-party systems.

Abstract

The monogamy is a fundamental property of Bell nonlocality and contextuality. In this article, we studied the $n$-cycle noncontextual inequalities and generalized CHSH inequalities in detail and found the sufficient conditions for those inequalities to be hold. According to those conditions, we provide several kind of tradeoff relations: monogamy of generalized Bell inequalities in non-signaling framework, monogamy of cycle type noncontextual inequalities and monogamy between Bell inequality and noncontextual inequality in general no-disturbance framework. At last, some generic tradeoff relations of generalized CHSH inequalities for $n$-party physical systems, which are beyond one-to-many scenario, are discussed.