Quantum key distribution rates from semidefinite programming

Understand

Computing the key rate in quantum key distribution (QKD) protocols is a long standing challenge.

• Analytical methods are limited to a handful of protocols with highly symmetric measurement bases.
• Numerical methods can handle arbitrary measurement bases, but either use the min-entropy, which gives a loose lower bound to the von Neumann entropy, or rely on cumbersome dedicated algorithms.
• Based on a recently discovered semidefinite programming (SDP) hierarchy converging to the conditional von Neumann entropy, used for computing the asymptotic key rates in the device independent case, we introduce an SDP hierarchy that converges to the asymptotic secret key rate in the case of characterised devices.