Not all entangled states violate Leggett's crypto-nonlocality

TL;DR

This paper clarifies that not all entangled states violate Leggett's crypto-nonlocality, emphasizing the importance of the original axioms and distinguishing it from quantum separability and local causality.

Contribution

It demonstrates that, under Leggett's original axioms, some entangled states are compatible with crypto-nonlocality, challenging previous claims that all entangled states violate it.

Findings

Some entangled states do not violate Leggett's crypto-nonlocality

Leggett's crypto-nonlocality is distinct from quantum separability

Clarifies the relation between crypto-nonlocality and local causality

Abstract

This note is a reply to M. Navascu\'es' claim that "all entangled states violate Leggett's crypto-nonlocality" [arXiv:1303.5124v2]. I argue that such a conclusion can only be reached if one introduces additional assumptions that further restrict Leggett's notion of "crypto-nonlocality". If a contrario one sticks only to Leggett's original axioms, there exist entangled states whose correlations are always compatible with Leggett's crypto-nonlocality---which is thus a genuinely different concept from quantum separability. I clarify in this note the relation between these two notions, together also with Bell's assumption of local causality.