Quantum communication and fault-tolerance

TL;DR

This thesis explores the limits of quantum communication, focusing on capacities and coding schemes with or without entanglement and noise, to understand how quantum channels can be used reliably.

Contribution

It investigates quantum communication capacities and coding strategies under various noise and entanglement assumptions, advancing understanding of quantum channel limits.

Findings

Quantum entanglement enhances communication capacity.

Noise impacts the achievable rates of quantum channels.

Optimal coding schemes depend on entanglement and noise models.

Abstract

In this thesis, we are interested in the limits of quantum communication with and without entanglement, and with and without noise assumptions on the communication setup. When a sender and a receiver are connected by a communication line that is governed by noise which is modelled by a quantum channel, they hope to design a coding scheme, i.e. messages and message decoders, in such a way that they are robust to this noise. The amount of message bits per channel use is called the achievable rate of the coding scheme, and the maximal achievable rate for a given quantum channel is called capacity of the quantum channel. Here, we are interested in coding schemes and capacities under various assumptions, in particular in the case where the sender and the receiver share quantum entanglement, which turns out to be the most natural generalization of the classical communication analogue that lies at the basis of many of our modern technologies.