Consequences and applications of the completeness of Hardy's nonlocality

TL;DR

This paper explores the implications of Hardy's paradox in quantum nonlocality, providing algorithms, characterizations of entangled states, and conditions for logical nonlocality in quantum systems.

Contribution

It offers new polynomial algorithms for deciding logical nonlocality, characterizes entangled states related to Hardy's paradox, and establishes conditions for witnessing nonlocality.

Findings

Polynomial algorithms for logical nonlocality decision

Bell states are uniquely non-logically nonlocal among two-qubit entangled states

Hardy nonlocality can be witnessed with certainty in tripartite systems

Abstract

Logical nonlocality is completely characterized by Hardy's "paradox" in (2,2,l) and (2,k,2) scenarios. We consider a variety of consequences and applications of this fact. (i) Polynomial algorithms may be given for deciding logical nonlocality in these scenarios. (ii) Bell states are the only entangled two-qubit states which are not logically nonlocal under projective measurements. (iii) It is possible to witness Hardy nonlocality with certainty in a simple tripartite quantum system. (iv) Noncommutativity of observables is necessary and sufficient for enabling logical nonlocality.