Mathematica Slovaca

Linear algebraic proof of Wigner theorem and its consequences

Jáchym Barvínek, Jan Hamhalter

Published Apr 1, 2017• 6 citations

Abstract

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.

DOI: 10.1515/ms-2016-0273

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