Enhanced quantum violation of a non-contextual inequality and witnessing quantum dimension

TL;DR

This paper derives the maximum quantum violation of a non-contextual inequality in sequential measurements, showing that increasing projectors enhances violation and can serve as a quantum dimension witness.

Contribution

It introduces the concept of degeneracy-breaking measurements and demonstrates how increasing projectors improves quantum violation and witnesses quantum dimension.

Findings

Quantum violation can reach the algebraic maximum with more projectors.

Optimal violations serve as quantum dimension witnesses.

Violation enhancement does not depend on system dimension.

Abstract

We consider a non-contextual inequality in the sequential measurement scenario and derive the optimal quantum violation of it without assuming the dimension of the system. Since the measurement is dichotomic and the dimension of the quantum system is arbitrary, we formulate the concept of degeneracy-breaking (DB) measurement depending on how many projectors are being used in the sequential measurement. We demonstrate that by increasing the number of projectors involved in the sequential measurement (thereby making the measurement more degeneracy breaking) the quantum violation of non-contextual inequality can be enhanced and can even reach up to its algebraic maximum. We demonstrate that the optimal quantum violations for different number of projectors serves as a quantum dimension witness.