Related papers: Infinite dimensional dynamical maps

Infinite dimensional dynamical maps

URL: http://arxiv.org/abs/2406.19176v1
Date: Thu, 27 Jun 2024 13:52:50 GMT
Title: Infinite dimensional dynamical maps
Authors: Bihalan Bhattacharya, Uwe Franz, Saikat Patra, Ritabrata Sengupta,
Abstract summary: We study whether a given system of dynamical maps is Markovian or non-Markovian. We construct several examples where the underlying Hilbert space may not be of finite dimensional.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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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