TY - JOUR
T1 - Universal bound on the eigenvalues of 2-positive trace-preserving maps
AU - vom Ende, Frederik
AU - Chruściński, Dariusz
AU - Kimura, Gen
AU - Muratore-Ginanneschi, Paolo
N1 - Publisher Copyright:
© 2025 Elsevier Inc.
PY - 2026/2/1
Y1 - 2026/2/1
N2 - 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.
AB - 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.
KW - 2-positivity
KW - Complete positivity
KW - Eigenvalue inequality
KW - Quantum-dynamical semigroup
KW - Relaxation rates
UR - https://www.scopus.com/pages/publications/105019641482
UR - https://www.scopus.com/pages/publications/105019641482#tab=citedBy
U2 - 10.1016/j.laa.2025.10.022
DO - 10.1016/j.laa.2025.10.022
M3 - Article
AN - SCOPUS:105019641482
SN - 0024-3795
VL - 730
SP - 262
EP - 275
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
ER -