Non-locality breaking qubit channels

TL;DR

This paper explores the concept of non-locality breaking in qubit channels, providing new criteria for when channels prevent CHSH nonlocality and characterizing strongly non-locality breaking channels.

Contribution

It introduces a necessary and sufficient condition for hidden CHSH nonlocality and characterizes all strongly non-locality breaking qubit channels, expanding understanding of nonlocality in quantum channels.

Findings

Unital qubit channels breaking nonlocality are strongly non-locality breaking.

Extremal qubit channels are not strongly non-locality breaking unless entanglement breaking.

Provided a closed-form condition for hidden CHSH nonlocality.

Abstract

Entanglement breaking channels play a significant role in quantum information theory. In this work we investigate qubit channels through their property of `non-locality breaking', defined in a natural way but within the purview of CHSH nonlocality. This also provides a different perspective on the relationship between entanglement and nonlocality through the dual picture of quantum channels instead of through states. For a channel to be entanglement breaking it is sufficient to `break' the entanglement of maximally entangled states. We provide examples to show that for CHSH nonlocality breaking such a property does not hold in general, though for certain channels and for a restricted class of states for all channels this holds.We also consider channels whose output remains local under SLOCC and call them `strongly non-locality breaking'. We provide a closed form necessary-sufficient condition for any two-qubit state to show hidden CHSH nonlocality, which is likely to be useful for other purposes as well. This in turn allows us to characterize all strongly non-locality breaking qubit channels. It turns out that unital qubit channels breaking nonlocality of maximally entangled states are strongly non-locality breaking while extremal qubit channels cannot be so unless they are entanglement breaking.