Sequential decoding of a general classical-quantum channel

TL;DR

This paper proves that sequential decoding strategies can reliably communicate over classical-quantum channels in the one-shot regime, even with multiple measurements that typically disturb quantum states.

Contribution

It generalizes a non-commutative union bound for sequences of measurements and demonstrates methods for state recovery after decoding, advancing quantum communication theory.

Findings

Sequential decoding works well in the one-shot regime.

A generalized non-commutative union bound is established.

Methods for state recovery after measurements are proposed.

Abstract

Since a quantum measurement generally disturbs the state of a quantum system, one might think that it should not be possible for a sender and receiver to communicate reliably when the receiver performs a large number of sequential measurements to determine the message of the sender. We show here that this intuition is not true, by demonstrating that a sequential decoding strategy works well even in the most general "one-shot" regime, where we are given a single instance of a channel and wish to determine the maximal number of bits that can be communicated up to a small failure probability. This result follows by generalizing a non-commutative union bound to apply for a sequence of general measurements. We also demonstrate two ways in which a receiver can recover a state close to the original state after it has been decoded by a sequence of measurements that each succeed with high probability. The second of these methods will be useful in realizing an efficient decoder for fully quantum polar codes, should a method ever be found to realize an efficient decoder for classical-quantum polar codes.