Bridging Resource Theory and Quantum Key Distribution: Geometric Analysis and Statistical Testing

TL;DR

This paper integrates resource theory with geometric and statistical analysis to evaluate quantum versus classical correlations in a QKD protocol, providing tools to assess nonclassicality and protocol quality.

Contribution

It introduces a novel geometric framework for analyzing QKD protocols using resource theory and develops statistical tests to measure deviations from classical behaviors.

Findings

Geometric analysis of the non-convex polytope for classical behaviors.

Statistical test for quantifying the distance between behaviors.

Linking deviations to quantum resource quality.

Abstract

Discerning between quantum and classical correlations is of great importance. Bell polytopes are well established as a fundamental tool. In this paper, we extend this line of inquiry by applying resource theory within the context of Network scenarios, to a Quantum Key Distribution (QKD) protocol. To achieve this, we consider the causal structure $P3$ that can describe the protocol, and we aim to develop useful statistical tests to assess it. More concretely, our objectives are twofold: firstly, to utilise the underlying causal structure of the QKD protocol to obtain a geometrical analysis of the resulting non-convex polytope, with a focus on the classical behaviours. Second, we devise a test within this framework to evaluate the distance between any two behaviours within the generated polytope. This approach offers a unique perspective, linking deviations from expected behaviour directly to the quality of the quantum resource or the residual nonclassicality in protocol execution.