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Linear algebraic proof of Wigner theorem and its consequences

  • Jáchym Barvínek and Jan Hamhalter EMAIL logo
Published/Copyright: April 28, 2017
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Abstract

We present new proof of non-bijective Wigner theorem on symmetries of quantum systems using only basic linear algebra. It is based on showing that any non-zero Jordan ∗-homomorphism between matrix algebras preserving rank-one projections is implemented by either a unitary or an anitiunitary map. As a new application we extend hitherto known results on preservers of quantum relative entropy to infinite quantum systems.


(Communicated by Sylvia Pullmanová)


Acknowledgement

The authors would like to thank to the referee for many valuable suggestions, especially for pointing out to gaps in the arguments. It enabled to improve earlier version of the paper significantly.

This work was supported by the “Grant Agency of the Czech Republic” grant number P201/12/0290, “Topological and geometrical properties of Banach spaces and operator algebras”.

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Received: 2014-4-14
Accepted: 2015-5-15
Published Online: 2017-4-28
Published in Print: 2017-4-25

© 2017 Mathematical Institute Slovak Academy of Sciences

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