Entanglement without hidden nonlocality

TL;DR

This paper investigates whether all entangled states can exhibit nonlocality after local filtering and demonstrates that some entangled states, like certain Werner states, cannot violate Bell inequalities even after filtering, revealing limits of hidden nonlocality.

Contribution

It proves that not all entangled states show hidden nonlocality, specifically identifying Werner states that maintain local hidden variable models despite filtering.

Findings

Certain Werner states do not violate Bell inequalities after filtering

Not all entangled states exhibit hidden nonlocality

Limits of local filtering in revealing nonlocality are established

Abstract

We consider Bell tests in which the distant observers can perform local filtering before testing a Bell inequality. Notably, in this setup, certain entangled states admitting a local hidden variable model in the standard Bell scenario can nevertheless violate a Bell inequality after filtering, displaying so-called hidden nonlocality. Here we ask whether all entangled states can violate a Bell inequality after well-chosen local filtering. We answer this question in the negative by showing that there exist entangled states without hidden nonlocality. Specifically, we prove that some two-qubit Werner states still admit a local hidden variable model after any possible local filtering on a single copy of the state.