Sequential decoding of a general classical-quantum channel

Understand

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.