Linear algebraic proof of Wigner theorem and its consequences

Year, pages: 2017, 371 - 386

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.

Barvínek, J., Hamhalter, J. 2017. Linear algebraic proof of Wigner theorem and its consequences. In Mathematica Slovaca, vol. 67, no.2, pp. 371-386. 0139-9918. DOI: https://doi.org/10.1515/ms-2016-0273

Barvínek, J., Hamhalter, J. (2017). Linear algebraic proof of Wigner theorem and its consequences. Mathematica Slovaca, 67(2), 371-386. 0139-9918. DOI: https://doi.org/10.1515/ms-2016-0273