Mapping the Schrodinger picture of open quantum dynamics

Abstract

For systems described by finite matrices, an affine form is developed for the maps that describe evolution of density matrices for a quantum system that interacts with another. This is established directly from the Heisenberg picture. It separates elements that depend only on the dynamics from those that depend on the state of the two systems. While the equivalent linear map is generally not completely positive, the homogeneous part of the affine maps is, and is shown to be composed of multiplication operations that come simply from the Hamiltonian for the larger system. The inhomogeneous part is shown to be zero if and only if the map does not increase the trace of the square of any density matrix. Properties are worked out in detail for two-qubit examples.

10 pages, 3 Figures, Accepted for publication in Phys. Rev. A

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• Entanglement increase from local interactions with not-completely-positive maps
• Geometry of depolarizing channels
• Non-perturbative treatment of open-system multi-time expectation values in Gaussian bosonic environments
• One qubit almost completely reveals the dynamics of two
• On the use of total state decompositions for the study of reduced dynamics
• Repeatable procedures and maps in open quantum dynamics
• George Sudarshan and Quantum Dynamics
• Decohering histories and open quantum systems