Secure key distribution based on Popescu-Rohrlich box fraction of dimensionally restricted nonlocality

TL;DR

This paper introduces a new measure of nonlocality called PR box fraction in a restricted Bell scenario, demonstrating its potential as a resource for secure key distribution without requiring entanglement certification.

Contribution

It defines the PR box fraction of dimensionally restricted nonlocality and shows its applicability for secure key distribution in a specific Bell scenario.

Findings

PR box fraction can be nonzero for Bell-local correlations.

Dimensionally restricted nonlocality ensures secrecy against restricted eavesdroppers.

PR box fraction can serve as a resource for secure key distribution without entanglement.

Abstract

For the bipartite Bell scenario with two inputs and two outputs, a nonlinear witness of dimensionally restricted nonlocality is introduced. Popescu-Rohrlich (PR) box fraction of dimensionally restricted nonlocality is then introduced and studied using the aforementioned witness and a nonlinear measure of correlations. This PR box fraction is also nonzero for certain Bell-local correlations. It is shown that any nonsignaling correlation shared by Alice and Bob that has dimensionally restricted nonlocality contains secrecy against any third party, Eve, who is also dimensionally restricted. In this context, for the specific Bell scenario considered, it is demonstrated that the PR box fraction of dimensionally restricted nonlocality can be used as a resource for secure quantum key distribution, even if entanglement is not certified.