Upper bounds on device-independent quantum key distribution rates in static and dynamic scenarios

TL;DR

This paper establishes new upper bounds on device-independent quantum key distribution rates, improving understanding of the limitations of DI-QKD protocols in static and dynamic scenarios, including channel capacities.

Contribution

It introduces convex and optimized bounds for DI-QKD key rates, enhancing the theoretical limits for protocols based on CHSH and quantum channels.

Findings

Convexity of reduced cc-squashed entanglement established

Tighter bounds for CHSH-based DI-QKD key rates derived

Upper bounds for DI private capacity on depolarizing and erasure channels obtained

Abstract

In this work, we develop upper bounds for key rates for device-independent quantum key distribution (DI-QKD) protocols and devices. We study the reduced cc-squashed entanglement and show that it is a convex functional. As a result, we show that the convex hull of the currently known bounds is a tighter upper bound on the device-independent key rates of standard CHSH-based protocol. We further provide tighter bounds for DI-QKD key rates achievable by any protocol applied to the CHSH-based device. This bound is based on reduced relative entropy of entanglement optimized over decompositions into local and non-local parts. In the dynamical scenario of quantum channels, we obtain upper bounds for device-independent private capacity for the CHSH based protocols. We show that the device-independent private capacity for the CHSH based protocols on depolarizing and erasure channels is limited by the secret key capacity of dephasing channels.