Entanglement transmission and generation under channel uncertainty: Universal quantum channel coding

TL;DR

This paper establishes the optimal rates for universal quantum codes that reliably transmit and generate entanglement over uncertain channels, extending quantum coding theory to compound channels with various information scenarios.

Contribution

It determines the capacities of compound quantum channels for entanglement transmission and generation, including informed decoder and encoder cases, advancing quantum communication under channel uncertainty.

Findings

Capacities of compound quantum channels for entanglement transmission and generation are equal.

Derived capacity formulas for scenarios with informed decoder or encoder.

Provided fundamental limits for universal quantum coding under channel uncertainty.

Abstract

We determine the optimal rates of universal quantum codes for entanglement transmission and generation under channel uncertainty. In the simplest scenario the sender and receiver are provided merely with the information that the channel they use belongs to a given set of channels, so that they are forced to use quantum codes that are reliable for the whole set of channels. This is precisely the quantum analog of the compound channel coding problem. We determine the entanglement transmission and entanglement-generating capacities of compound quantum channels and show that they are equal. Moreover, we investigate two variants of that basic scenario, namely the cases of informed decoder or informed encoder, and derive corresponding capacity results.