Secret Message Transmission over Quantum Channels under Adversarial Quantum Noise: Secrecy Capacity and Super-Activation

TL;DR

This paper analyzes the secrecy capacity of arbitrarily varying quantum channels under adversarial noise, establishing conditions for continuity, and demonstrating super-activation where combined channels enable secure communication despite individual zero capacities.

Contribution

It introduces a unified code construction for secrecy capacity under different error criteria and proves the super-activation phenomenon for AVQCs, advancing understanding of secure quantum communication.

Findings

Secrecy capacities are characterized for AVQCs under average and maximal error probabilities.

Super-activation occurs when two zero-capacity channels combine to enable positive secure transmission.

The paper identifies conditions for the continuity and discontinuity of secrecy capacities.

Abstract

We determine the secrecy capacities of AVQCs (arbitrarily varying quantum channels). Both secrecy capacity with average error probability and with maximal error probability are derived. Both derivations are based on one common code construction. The code we construct fulfills a stringent secrecy requirement, which is called the strong code concept. We determine when the secrecy capacity is a continuous function of the system parameters and completely characterize its discontinuity points both for average error criterion and for maximal error criterion. Furthermore, we prove the phenomenon "super-activation" for secrecy capacities of AVQCs, i.e., two quantum channels both with zero secrecy capacity, which, if used together, allow secure transmission with positive capacity. We also discuss the relations between the entanglement distillation capacity, the entanglement generating capacity, and the strong subspace transmission capacity for AVQCs.