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

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