## On partially trace distance preserving maps and reversible quantum channels.(English)Zbl 1397.81031

Summary: We give a characterization of trace-preserving and positive linear maps preserving trace distance partially, that is, preservers of trace distance of quantum states or pure states rather than all matrices. Applying such results, we give a characterization of quantum channels leaving Helstrom’s measure of distinguishability of quantum states or pure states invariant and show that such quantum channels are fully reversible, which are unitary transformations.

### MSC:

 81P16 Quantum state spaces, operational and probabilistic concepts 81P45 Quantum information, communication, networks (quantum-theoretic aspects)
Full Text: