Upper bounds on device-independent quantum key distribution

TL;DR

This paper establishes upper bounds on the rate of device-independent quantum key distribution (DIQKD), showing that DIQKD can be significantly less efficient than standard QKD for certain states and channels.

Contribution

It provides the first upper bounds on DIQKD rates, demonstrating scenarios where DIQKD is substantially less effective than traditional QKD.

Findings

Upper bounds on DIQKD rates surpass those for standard QKD.

Existence of states and channels with high QKD but negligible DIQKD rates.

Practical implications for entangled two-qubit states using standard post-processing.

Abstract

Quantum key distribution (QKD) is a method that distributes a secret key to a sender and a receiver by the transmission of quantum particles (e.g. photons). Device-independent quantum key distribution (DIQKD) is a version of QKD with a stronger notion of security, in that the sender and receiver base their protocol only on the statistics of input and outputs of their devices as inspired by Bell's theorem. We study the rate at which DIQKD can be carried out for a given bipartite quantum state distributed between the sender and receiver or a quantum channel connecting them. We provide upper bounds on the achievable rate going beyond upper bounds possible for QKD. In particular, we construct states and channels where the QKD rate is significant while the DIQKD rate is negligible. This gap is illustrated for a practical case arising when using standard post-processing techniques for entangled two-qubit states.