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arXiv · 2507.11766

Notes on completely positive maps and continuous-time Markovian CP evolution. A geometry-flavored perspective

Paul E. Lammert
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Abstract

These notes provide a detailed and self-contained exposition of basic theory of CP maps and continuous-time Markovian evolution.The infinite-dimensional (separable) setting is handled as an extension of the finite-dimensional one.The treatment stands on two legs.For the finite-dimensional part, a basis-free version of the Choi-Jamiolkowski isomorphism called simply Jamiolkowski transform.And, for the extension, the ground matrix element topology (GMET), which does for the superoperators on trace-class operators what the weak-operator topology does for bounded operators on a Hilbert space. Background in open quantum systems or quantum information theory is not assumed.

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Paul E. Lammert. 2025-07-15. Notes on completely positive maps and continuous-time Markovian CP evolution. A geometry-flavored perspective. https://arxiv.org/abs/2507.11766

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