## Journal of Applied Mathematics

### On Partially Trace Distance Preserving Maps and Reversible Quantum Channels

#### Abstract

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.

#### Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 474291, 5 pages.

Dates
First available in Project Euclid: 14 March 2014

https://projecteuclid.org/euclid.jam/1394808160

Digital Object Identifier
doi:10.1155/2013/474291

Mathematical Reviews number (MathSciNet)
MR3115288

Zentralblatt MATH identifier
06950694

#### Citation

Jian, Long; He, Kan; Yuan, Qing; Wang, Fei. On Partially Trace Distance Preserving Maps and Reversible Quantum Channels. J. Appl. Math. 2013 (2013), Article ID 474291, 5 pages. doi:10.1155/2013/474291. https://projecteuclid.org/euclid.jam/1394808160

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