Quantum Bell nonlocality cannot be shared under a special kind of bilateral measurements for high-dimensional quantum states

TL;DR

This paper demonstrates that quantum Bell nonlocality cannot be shared under certain bilateral measurements in high-dimensional states, extending previous unilateral measurement results with analytical proofs and generalizable strategies.

Contribution

It introduces a specific class of projection operators showing nonshareability of Bell nonlocality under bilateral measurements, generalizable to higher dimensions.

Findings

Bell nonlocality cannot be shared under these measurements

Analytical proof provided for nonshareability

Measurement strategies are extendable to high-dimensional states

Abstract

Quantum Bell nonlocality is an important quantum phenomenon. Recently, the shareability of Bell nonlocality under unilateral measurements has been widely studied. In this study, we consider the shareability of quantum Bell nonlocality under bilateral measurements. Under a specific class of projection operators, we find that quantum Bell nonlocality cannot be shared for a limited number of times, as in the case of unilateral measurements. Our proof is analytical and our measurement strategies can be generalized to higher dimension cases.