Distillation of secret key from a class of compound memoryless quantum sources

TL;DR

This paper establishes the optimal secret-key distillation rates from classical-quantum-quantum sources under various knowledge scenarios, introducing universal protocols and highlighting the importance of source regularity for secure quantum communication.

Contribution

It introduces universally reliable and secure protocols for secret-key distillation from compound cqq sources and derives a multi-letter formula for the optimal capacity under regularity conditions.

Findings

Optimal secret-key capacity formula for regular cqq sources.

Capacity equality with and without sender’s marginal knowledge under regularity.

Example showing zero capacity without sender knowledge, positive with it.

Abstract

We consider secret-key distillation from tripartite compound classical-quantum-quantum (cqq) sources with free forward public communication under strong security criterion. We design protocols which are universally reliable and secure in this scenario. These are shown to achieve asymptotically optimal rates as long as a certain regularity condition is fulfilled by the the set of its generating density matrices. We derive a multi-letter formula which describes the optimal forward secret-key capacity for all compound cqq sources being regular in this sense. We also determine the forward secret-key distillation capacity for situations, where the legitimate sending party has perfect knowledge of his/her marginal state deriving from the source statistics. In this case regularity conditions can be dropped. Our results show that the capacities with and without the mentioned kind of state knowledge are equal as long as the source is generated by a regular set of density matrices. We demonstrate that regularity of cqq sources is not only a technical but also an operational issue. For this reason, we give an example of a source which has zero secret-key distillation capacity without sender knowledge, while achieving positive rates is possible if sender marginal knowledge is provided.