Bounding the persistency of the nonlocality of W states

TL;DR

This paper investigates how many particles must be removed from W states to destroy their nonlocality, providing bounds that grow proportionally with the total number of particles, and introduces a framework for more complex Bell tests.

Contribution

It establishes bounds on the minimal particle removal needed to make W states local, extending understanding of their nonlocality persistency and developing a framework for multiple settings.

Findings

The minimal number of particles to remove scales between 2N/5 and N/2 for large N.

W states retain nonlocality despite particle loss, indicating high persistency.

A new framework for analyzing nonlocality with more than two measurement settings per site.

Abstract

The nonlocal properties of the W states are investigated under particle loss. By removing all but two particles from an $N$-qubit W state, the resulting two-qubit state is still entangled. Hence, the W state has high persistency of entanglement. We ask an analogous question regarding the persistency of nonlocality introduced in [Phys. Rev. A 86, 042113]. Namely, we inquire what is the minimal number of particles that must be removed from the W state so that the resulting state becomes local. We bound this value in function of $N$ qubits by considering Bell nonlocality tests with two alternative settings per site. In particular, we find that this value is between $2N/5$ and $N/2$ for large $N$. We also develop a framework to establish bounds for more than two settings per site.