%0 electronic Article
%A Wilde, Mark M.
%D 2013
%G English
%@ 1364-5021
%T Sequential decoding of a general classical-quantum channel
%J Proceedings of the Royal Society of London
%V 469
%N 2157
%P 1-12
%U https://www.jstor.org/stable/43923643
%K research-article
%X Because 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.