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arXiv · 2109.10409

Canonical structures of $A$ and $B$ forms

Sudha·B. N. Karthik·A. R. Usha Devi·A. K. Rajagopal
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Abstract

In their seminal paper (Phys. Rev.121, 920 (1961)) Sudarshan, Mathews and Rau investigated properties of the dynamical $A$ and $B$ maps acting on $n$ dimensional quantum systems. Nature of the dynamical maps in open quantum system evolutions has attracted great deal of attention in the later years. However, the novel paper on the $A$ and $B$ dynamical maps has not received its due attention. In this tutorial article we review the properties of $A$ and $B$ forms associated with the dynamics of finite dimensional quantum systems. In particular we investigate a canonical structure associated with the $A$ form and establish its equivalence with the associated $B$ form. We show that the canonical structure of the $A$ form captures the completely positive (not completely positive) nature of the dynamics in a succinct manner. This feature is illustrated through physical examples of qubit channels.

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Sudha, B. N. Karthik, A. R. Usha Devi, A. K. Rajagopal. 2021-09-21. Canonical structures of $A$ and $B$ forms. https://doi.org/10.12743/quanta.v10i1.165

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