Reduction of Quantum Entropy by Reversible Extraction of Classical Information

We inquire under what conditions some of the information in a quantum signal source, namely a set of pure states a emitted with probabilities p a , can be extracted in classical form by a measurement leaving the quantum system with less entropy than it had before, but retaining the ability to regenerate the source state exactly from the classical measurement result and the after-measurement state of the quantum system. We show that this can be done if and only if the source states a fall into two or more mutually orthogonal subsets.