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. © 2013 The Authors.
Publication Source (Journal or Book title)
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Wilde, M. (2013). Sequential decoding of a general classical-quantum channel. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 469 (2157) https://doi.org/10.1098/rspa.2013.0259