@article{Tian2025, 
author = {Yulong Tian and Jinli Xu},
title = {Generalizations of Wigner's theorem from rank-   1 projections to rank-   n projections},
year = {2025},
journal = {Electronic Research Archive},
volume = {33},
number = {5},
pages = {3201-3209},
keywords = {Wigner's theorem, preserver, projections, transition probability},
url = {https://www.sciopen.com/article/10.3934/era.2025140},
doi = {10.3934/era.2025140},
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  :      P          1            (    H    )    →      P          n            (    K    )   multiplying    n times the transition probability and maps    ϕ  :      P          1            (    H    )    →      P          n            (    K    )   sending each complete orthogonal system of rank-   1 projections to some complete orthogonal system of rank-   n projections.}
}