Affine maps of density matrices

Abstract

For quantum systems described by finite matrices, linear and affine maps of matrices are shown to provide equivalent descriptions of evolution of density matrices for a subsystem caused by unitary Hamiltonian evolution in a larger system; an affine map can be replaced by a linear map, and a linear map can be replaced by an affine map. There may be significant advantage in using an affine map. The linear map is generally not completely positive, but the linear part of an equivalent affine map can be chosen to be completely positive and related in the simplest possible way to the unitary Hamiltonian evolution in the larger system.

4 pages, title changed, sentence added, reference updated

References in corpus (2)

• Dynamics of initially entangled open quantum systems
• Is the dynamics of open quantum systems always linear?

Cited by in corpus (10)

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• Symmetries in open quantum dynamics