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arXiv · 2406.19176

Infinite dimensional dynamical maps

Bihalan Bhattacharya·Uwe Franz·Saikat Patra·Ritabrata Sengupta
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Abstract

Completely positive trace preserving maps are widely used in quantum information theory. These are mostly studied using the master equation perspective. A central part in this theory is to study whether a given system of dynamical maps $\{\Lambda_t: t \ge 0\}$ is Markovian or non-Markovian. We study the problem when the underlying Hilbert space is of infinite dimensional. We construct a sufficient condition for checking P (resp. CP) divisibility of dynamical maps. We construct several examples where the underlying Hilbert space may not be of finite dimensional. We also give a special emphasis on Gaussian dynamical maps and get a version of our result in it.

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Bihalan Bhattacharya, Uwe Franz, Saikat Patra, Ritabrata Sengupta. 2024-06-27. Infinite dimensional dynamical maps. https://doi.org/10.1016/j.laa.2026.01.020

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