Linear algebraic proof of Wigner theorem and its consequences. (English) Zbl 1424.81005

Barvínek, Jáchym; Hamhalter, Jan

Math. Slovaca 67, No. 2, 371-386 (2017).

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.

Reviewer: Lajos Molnár (Szeged)

MSC:

81P45	Quantum information, communication, networks (quantum-theoretic aspects)
15A86	Linear preserver problems

Keywords:

Jordan homomorphisms; Wigner theorem; relative quantum entropy