Fundamental limits on key rates in device-independent quantum key distribution

TL;DR

This paper introduces measures of non-locality and steerability in quantum systems, establishing their properties and demonstrating they bound the secret-key capacities in device-independent and semi-device-independent quantum key distribution protocols.

Contribution

It defines intrinsic non-locality and intrinsic steerability, proving they are upper bounds on secret-key capacities and establishing their fundamental properties.

Findings

Intrinsic non-locality bounds secret-key capacity in device-independent protocols.

Intrinsic steerability bounds secret-key capacity in semi-device-independent protocols.

Intrinsic non-locality is bounded above by intrinsic steerability.

Abstract

In this paper, we introduce intrinsic non-locality as a quantifier for Bell non-locality, and we prove that it satisfies certain desirable properties such as faithfulness, convexity, and monotonicity under local operations and shared randomness. We then prove that intrinsic non-locality is an upper bound on the secret-key-agreement capacity of any device-independent protocol conducted using a device characterized by a correlation $p$. We also prove that intrinsic steerability is an upper bound on the secret-key-agreement capacity of any semi-device-independent protocol conducted using a device characterized by an assemblage $\hat{\rho}$. We also establish the faithfulness of intrinsic steerability and intrinsic non-locality. Finally, we prove that intrinsic non-locality is bounded from above by intrinsic steerability.