Towards an equivalence between maximal entanglement and maximal quantum nonlocality

TL;DR

This paper investigates the relationship between pure-state entanglement and nonlocality, demonstrating that for two-qubit states, higher entanglement correlates with increased likelihood of violating Bell inequalities under random measurements, and extends findings to multipartite states.

Contribution

It introduces and validates a measure of nonlocality based on the probability of violation under random measurements, showing its monotonic relation with entanglement for two-qubit states and extending to multipartite systems.

Findings

The measure satisfies natural properties of an operational nonlocality measure.

For two-qubit pure states, increased entanglement leads to higher violation probability.

Results are extended to multipartite quantum states.

Abstract

While all bipartite pure entangled states are known to generate correlations violating a Bell inequality, and are therefore nonlocal, the quantitative relation between pure-state entanglement and nonlocality is poorly understood. In fact, some Bell inequalities are maximally violated by non-maximally entangled states and this phenomenon is also observed for other operational measures of nonlocality. In this work, we study a recently proposed measure of nonlocality defined as the probability that a pure state displays nonlocal correlations when subjected to random measurements. We first prove that this measure satisfies some natural properties for an operational measure of nonlocality. Then, we show that for pure states of two qubits the measure is monotonic with entanglement for all correlation two-outcome Bell inequalities: for all these inequalities, the more the state is entangled, the larger the probability to violate them when random measurements are performed. Finally, we extend our results to the multipartite setting.