an:06725897
Zbl 1424.81005
Barv??nek, J??chym; Hamhalter, Jan
Linear algebraic proof of Wigner theorem and its consequences
EN
Math. Slovaca 67, No. 2, 371-386 (2017).
00366466
2017
j
81P45 15A86
Jordan homomorphisms; Wigner theorem; relative quantum entropy
The authors present one another proof of the non-bijective version of Wigner's famous theorem on the structure of quantum mechanical symmetry transformations. Basically, they apply only elementary linear algebra. The key point is to show that any non-zero Jordan *-homomorphism between matrix algebras preserving rank-one projections is implemented by either a unitary or an antiunitary operator. An application concerning certain preservers of quantum relative entropy on infinite quantum systems is also presented.
Lajos Moln??r (Szeged)