Tomiyama-type maps with a diagonal perturbation
Rings and Algebras
2026-04-22 v1 Operator Algebras
Quantum Physics
Abstract
We investigate a two-parameter family of linear maps on matrix algebras, constructed as diagonal perturbations of classical Tomiyama maps. Employing the Choi matrix method alongside block-positivity techniques, we derive explicit necessary and sufficient conditions for positivity, complete positivity, and k-positivity across arbitrary dimensions. These conditions provide a transparent geometric characterization of the positivity regions within the parameter space.
Keywords
Cite
@article{arxiv.2604.18600,
title = {Tomiyama-type maps with a diagonal perturbation},
author = {Anindita Bera and Bihalan Bhattacharya and Dariusz Chruściński},
journal= {arXiv preprint arXiv:2604.18600},
year = {2026}
}
Comments
16 pages, 4 figures, comments are welcome