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

Jian, Long; He, Kan; Yuan, Qing; Wang, Fei

J. Appl. Math. 2013, Article ID 474291, 5 p. (2013).

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)