Extremal Quantum Correlations and Cryptographic Security

TL;DR

This paper characterizes extremal quantum probability distributions as essential for device-independent security in quantum cryptography, providing algebraic criteria and verification schemes for secure distributions in multi-party scenarios.

Contribution

It establishes a precise link between extremal quantum distributions and security, offering a new algebraic characterization and practical verification methods.

Findings

Extremal quantum distributions are necessary and sufficient for device-independent security.

A scheme for verifying security in two-party, two-setting, two-outcome scenarios.

Application of the method to multi-party quantum cryptographic setups.

Abstract

We investigate a fundamental property of device independent security in quantum cryptography by characterizing probability distributions which are necessarily independent of the measurement results of any eavesdropper. We show that probability distributions that are secure in this sense are exactly the extremal quantum probability distributions. This allows us to give a characterization of security in algebraic terms. We apply the method to common examples for two-party as well as multi-party setups and present a scheme for verifying security of probability distributions with two parties, two measurement settings, and two outcomes.