Generalizations of Wigner’s theorem from rank-1 projections to rank-n projections

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Abstract

We provide generalizations of the classical Wigner’s theorem as well as Uhlhorn’s version of Wigner’s theorem by considering maps that send rank-1 projections to rank-n projections. Namely, we describe the general form of maps ϕ :P₁(H) → P_n(K) multiplying n times the transition probability and maps ϕ : P₁(H) → P_n(K) sending each complete orthogonal system of rank-1 projections to some complete orthogonal system of rank-n projections.

Keywords

Wigner’s theorem / preserver / projections / transition probability

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