Entanglement Transmission over Arbitrarily Varying Quantum Channels

TL;DR

This paper establishes a formula for the entanglement transmission capacity of arbitrarily varying quantum channels, demonstrating a quantum analog of the Ahlswede dichotomy and exploring symmetrizability concepts.

Contribution

It provides a regularized capacity formula for AVQCs, proves the equivalence of random and deterministic capacities under certain conditions, and introduces definitions of symmetrizability for these channels.

Findings

Capacity formula for finite AVQCs derived

Random and deterministic capacities are equal under certain conditions

Introduces two definitions of symmetrizability for AVQCs

Abstract

We derive a regularized formula for the common randomness assisted entanglement transmission capacity of finite arbitrarily varying quantum channels (AVQC's). For finite AVQC's with positive capacity for classical message transmission we show, by derandomization through classical forward communication, that the random capacity for entanglement transmission equals the deterministic capacity for entanglement transmission. This is a quantum version of the famous Ahlswede dichotomy. In the infinite case, we derive a similar result for certain classes of AVQC's. At last, we give two possible definitions of symmetrizability of an AVQC.