Multiple Observers Can Share the Nonlocality of Half of an Entangled Pair by Using Optimal Weak Measurements

TL;DR

This paper explores how multiple observers can sequentially share the nonlocal correlations of an entangled pair by employing optimal weak measurements that balance information gain and disturbance, leading to repeated Bell inequality violations.

Contribution

It introduces a method to share nonlocality among many observers using optimal weak measurements, extending the understanding of quantum nonlocality sharing.

Findings

Multiple observers can sequentially violate the CHSH-Bell inequality.

Optimal weak measurements enable sharing of nonlocality without destroying entanglement.

Arbitrarily long sequences of Bell violations are possible with the right measurement strategy.

Abstract

We investigate the trade-off between information gain and disturbance for a class of weak von Neumann measurements on spin-$\frac{1}{2}$ particles, and derive the unusual measurement pointer state that saturates this trade-off. We then consider the fundamental question of sharing the non-locality of a single particle of an entangled pair among multiple observers, and demonstrate that by exploiting the information gain disturbance trade-off, one can obtain an arbitrarily long sequence of consecutive and independent violations of the CHSH-Bell inequality.