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

Sharing tripartite nonlocality sequentially using only projective measurements

“…Furthermore, the bilateral sharing of nonlocality for two-qubit entangled states [27,28] and the trilateral nonlocality sharing for three-qubit entangled states [29] have also been studied. So far, significant progress has been made in the study of nonlocality sharing along this line of research [30][31][32][33][34][35][36].…”