Karol

In this work, we develop upper bounds for key rates for device-independent key distribution protocols, devices, and channels. 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 DIQKD 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 scenario of quantum channels, we obtain upper bounds for device-independent private capacity for the CHSH based protocols. We show that the DI private capacity for the CHSH based protocols on depolarizing and erasure channels is limited by the secret key capacity of dephasing channels.