Classical-Quantum Arbitrarily Varying Wiretap Channel: Ahlswede dichotomy, Positivity, Resources, Super Activation

TL;DR

This paper proves a dichotomy for classical-quantum wiretap channels, showing their secrecy capacity is either zero or equals the randomness-assisted capacity, and demonstrates super-activation with resource sharing.

Contribution

It establishes Ahlswede dichotomy for these channels and reveals super-activation phenomena, highlighting the importance of resources like randomness for secure communication.

Findings

Secrecy capacity is either zero or equals the randomness-assisted capacity.

Resources such as randomness and correlation enhance positive secrecy capacity.

Super-activation allows secure transmission when combining two zero-capacity channels.

Abstract

We establish Ahlswede dichotomy for arbitrarily varying classical-quantum wiretap channels. This means that either the deterministic secrecy capacity of an arbitrarily varying classical-quantum wiretap channel is zero or it equals its randomness-assisted secrecy capacity. We analyze the secrecy capacity of arbitrarily varying classical-quantum wiretap channels when the sender and the receiver use various resources. It turns out that having randomness, common randomness, and correlation as resources are very helpful for achieving a positive deterministic secrecy capacity of arbitrarily varying classical-quantum wiretap channels. We prove the phenomenon super-activation for arbitrarily varying classical-quantum wiretap channels, i.e., if we use two arbitrarily varying classical-quantum wiretap channels, both with zero deterministic secrecy capacity together, they allow perfect secure transmission.