Min-entropy and quantum key distribution: non-zero key rates for "small" numbers of signals

TL;DR

This paper calculates secret key rates for quantum key distribution with finite signals using min-entropy, showing non-zero rates for fewer signals than previous methods, and improves these rates through parameter estimation modifications.

Contribution

It explicitly evaluates min-entropy for finite signals in quantum key distribution, demonstrating improved key rates and revealing insights into measurement optimality for symmetric states.

Findings

Non-zero key rates for 10^4-10^5 signals.

Explicit calculation of min-entropy in finite-signal QKD.

Optimal measurement strategy for symmetric tensor product states.

Abstract

We calculate an achievable secret key rate for quantum key distribution with a finite number of signals, by evaluating the min-entropy explicitly. The min-entropy can be expressed in terms of the guessing probability, which we calculate for d-dimensional systems. We compare these key rates to previous approaches using the von Neumann entropy and find non-zero key rates for a smaller number of signals. Furthermore, we improve the secret key rates by modifying the parameter estimation step. Both improvements taken together lead to non-zero key rates for only 10^4-10^5 signals. An interesting conclusion can also be drawn from the additivity of the min-entropy and its relation to the guessing probability: for a set of symmetric tensor product states the optimal minimum-error discrimination (MED) measurement is the optimal MED measurement on each subsystem.