Related papers: Universal Bound on the Eigenvalues of 2-Positive Trace-Preserving Maps

Universal Bound on the Eigenvalues of 2-Positive Trace-Preserving Maps

URL: http://arxiv.org/abs/2506.02145v1
Date: Mon, 02 Jun 2025 18:18:00 GMT
Title: Universal Bound on the Eigenvalues of 2-Positive Trace-Preserving Maps
Authors: Frederik vom Ende, Dariusz Chruściński, Gen Kimura, Paolo Muratore-Ginanneschi,
Abstract summary: We prove an upper bound on the trace of any 2-positive, trace-preserving map in terms of its smallest eigenvalue.<n>We show that 2-positivity is necessary for this inequality to hold in general.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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.

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