Unifying Two Notions of Nonlocality in Quantum Theory

TL;DR

This paper unifies two types of nonlocality in quantum theory—nonlocality without entanglement and Bell-nonlocality—by analyzing how global unitaries affect the distinguishability and entanglement of quantum states.

Contribution

It introduces a unified framework to quantify nonlocality in quantum ensembles through the effect of global unitaries on state properties, linking two previously separate notions.

Findings

CNOT operation creates entanglement if and only if bases become irreducible under LOCC.

The proposed criteria quantify nonlocality even in incomplete product state sets.

More nonlocality can be associated with less entanglement, explaining certain quantum phenomena.

Abstract

Ensembles containing orthogonal product states are found to be indistinguishable under local operations and classical communication (LOCC), thereby showing irreversibility in the preparation and distinguishing processes, which is commonly known as nonlocality without entanglement. On the other hand, correlations arising from incompatible measurements on entangled states lead to Bell-nonlocality. We unify these two concepts from the change in certain property incurred in the ensemble under a suitable global unitary transformation. Specifically, we prove that under controlled-NOT (CNOT) operation, a full product basis can create entangled states if and only if the full bases or any subspace of it become irreducible in the process of LOCC discrimination. The proposed criteria quantifies the amount of nonlocality associated with the sets of product states which are even incomplete. For a set having entangled states, we modify the quantity accordingly and show that it can provide an explanation for the phenomena of more nonlocality with less entanglement.