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Mathematica Slovaca

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Volume 67, Issue 2


Linear algebraic proof of Wigner theorem and its consequences

Jáchym Barvínek
  • Department of Mathematics Faculty of Electrical Engineering Czech Technical University in Prague Technická 2 166 27 Prague 6 Czech Republic
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Jan Hamhalter
  • Department of Mathematics Faculty of Electrical Engineering Czech Technical University in Prague Technická 2 166 27 Prague 6 Czech Republic
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  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2017-04-28 | DOI: https://doi.org/10.1515/ms-2016-0273


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.

Keywords: Jordan homomorphisms; Wigner theorem; relative quantum entropy

MSC 2010: Primary 15A86; Secondary 81P45


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About the article

Received: 2014-04-14

Accepted: 2015-05-15

Published Online: 2017-04-28

Published in Print: 2017-04-25

Citation Information: Mathematica Slovaca, Volume 67, Issue 2, Pages 371–386, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2016-0273.

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