Universal Bound on the Eigenvalues of 2-Positive Trace-Preserving Maps
Rings and Algebras
2025-10-29 v1 Mathematical Physics
Dynamical Systems
math.MP
Quantum Physics
Abstract
We prove an upper bound on the trace of any 2-positive, trace-preserving map in terms of its smallest eigenvalue. We show that this spectral bound is tight, and that 2-positivity is necessary for this inequality to hold in general. Moreover, we use this to infer a similar bound for generators of one-parameter semigroups of 2-positive trace-preserving maps. With this approach we generalize known results for completely positive trace-preserving dynamics while providing a significantly simpler proof that is entirely algebraic.
Keywords
Cite
@article{arxiv.2506.02145,
title = {Universal Bound on the Eigenvalues of 2-Positive Trace-Preserving Maps},
author = {Frederik vom Ende and Dariusz Chruściński and Gen Kimura and Paolo Muratore-Ginanneschi},
journal= {arXiv preprint arXiv:2506.02145},
year = {2025}
}
Comments
11+6 pages, to be submitted to Linear Algebra Appl.; comments welcome