A generalization of the Choi isomorphism with application to open quantum systems

2024/08/06 by Heinz-Jürgen Schmidt, Heinz–Jürgen Schmidt, Schmidt, Heinz-Jürgen · 1 citation
Mathematics · #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.1515/zna-2026-0002

Abstract

Abstract Completely positive transformations play an important role in the description of state changes in quantum mechanics, including the time evolution of open quantum systems. One useful tool to describe them is the so-called Choi isomorphism, which maps completely positive transformations to positive semi-definite matrices. Accordingly, there are numerous proposals to generalize the Choi isomorphism. In the present paper, we show that the 1976 paper of Gorini, Kossakowski, and Sudarshan (GKS) already holds the key for a further generalization and study the resulting GKS isomorphism. As an application, we compute the GKS matrix of the time evolution of a general open quantum system up to second order in time.

Citations

• Completely positive dynamical semigroups of <i>N</i>-level systems
• Completely positive linear maps on complex matrices

Cited by

• Quantum orientation, Noether structure, composition of systems and operations

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