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arXiv · 2506.02145

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

Frederik vom Ende·Dariusz Chruściński·Gen Kimura·Paolo Muratore-Ginanneschi
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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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Frederik vom Ende, Dariusz Chruściński, Gen Kimura, Paolo Muratore-Ginanneschi. 2025-06-02. Universal Bound on the Eigenvalues of 2-Positive Trace-Preserving Maps. https://doi.org/10.1016/j.laa.2025.10.022

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