Canonical Structure of A and B Maps

Sudha Sudha, B. N. Karthik, A. R. Usha Devi, A. K. Rajagopal


In their seminal 1961 paper, Sudarshan, Mathews and Rau investigated properties of the dynamical A and B maps acting on n-dimensional quantum systems. The nature of 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.

Quanta 2021; 10: 34–41.

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ISSN: 1314-7374