Maps preserving transition probability from pure product states to pure states

Abstract

ABSTRACT Let n>1 be a positive integer, {H 1, …, H n } be a finite collection of complex Hilbert spaces with , and P 1(H k ) be the set of all rank-1 self-adjoint projections on H k , k = 1, …, n. Set We characterize the maps ϕ from to preserving transition probability, i.e. A particular case corresponding to n = 1 is well known as (non-surjective version) Wigner's theorem. Our result may be considered as a generalization of Wigner's theorem.