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

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.

24 pages

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• Upper bounds on key rates in device-independent quantum key distribution based on convex-combination attacks
• Testing of quantum nonlocal correlations under constrained free will and imperfect detectors
• Optimal quantum precision in noise estimation: Is entanglement necessary?
• Squashed quantum non-Markovianity: a measure of genuine quantum non-Markovianity in states