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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 474291, 5 pages
Research Article

On Partially Trace Distance Preserving Maps and Reversible Quantum Channels

College of Mathematics, Institute of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi 030024, China

Received 24 July 2013; Accepted 15 September 2013

Academic Editor: Francis T. K. Au

Copyright © 2013 Long Jian et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.