Fault-tolerant Coding for Entanglement-Assisted Communication

TL;DR

This paper extends fault-tolerant quantum channel coding to entanglement-assisted communication, showing that capacity approaches the ideal as gate errors diminish, and introduces fault-tolerant entanglement distillation.

Contribution

It develops fault-tolerant coding schemes for entanglement-assisted quantum communication, demonstrating capacity convergence and introducing a novel fault-tolerant entanglement distillation method.

Findings

Fault-tolerant capacity approaches standard capacity as gate errors go to zero.

Introduces fault-tolerant entanglement distillation technique.

Techniques are modular and adaptable to other fault-tolerant communication scenarios.

Abstract

Channel capacities quantify the optimal rates of sending information reliably over noisy channels. Usually, the study of capacities assumes that the circuits which sender and receiver use for encoding and decoding consist of perfectly noiseless gates. In the case of communication over quantum channels, however, this assumption is widely believed to be unrealistic, even in the long-term, due to the fragility of quantum information, which is affected by the process of decoherence. Christandl and M\"uller-Hermes have therefore initiated the study of fault-tolerant channel coding for quantum channels, i.e. coding schemes where encoder and decoder circuits are affected by noise, and have used techniques from fault-tolerant quantum computing to establish coding theorems for sending classical and quantum information in this scenario. Here, we extend these methods to the case of entanglement-assisted communication, in particular proving that the fault-tolerant capacity approaches the usual capacity when the gate error approaches zero. A main tool, which might be of independent interest, is the introduction of fault-tolerant entanglement distillation. We furthermore focus on the modularity of the techniques used, so that they can be easily adopted in other fault-tolerant communication scenarios.