Completely positive maps within the framework of direct-sum decomposition of state space
arXiv:1407.2051 · doi:10.1103/PhysRevA.90.012305
Abstract
We investigate completely positive maps for an open system interacting with its environment. The families of the initial states for which the reduced dynamics can be described by a completely positive map are identified within the framework of direct-sum decomposition of state space. They includes not only separable states with vanishing or nonvanishing quantum discord but also entangled states. A general expression of the families as well as the Kraus operators for the completely positive maps are explicitly given. It significantly extends the previous results.
7 pages, no figure
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- Effects of initial system-environment correlations on open quantum system dynamics and state preparation
- Reduced dynamical maps in the presence of initial correlations
- Initial Correlations in Open Quantum Systems: Constructing Linear Dynamical Maps and Master Equations
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- Reference state for arbitrary U-consistent subspace
- Sufficient Conditions and Constraints for Reversing General Quantum Errors
- Markovianity of the reference state, complete positivity of the reduced dynamics, and monotonicity of the relative entropy
- When the assignment map is completely positive
- Requiring linearity leads to complete positivity
- Positivity of the assignment map implies complete positivity of the reduced dynamics
- Guaranteeing Completely Positive Quantum Evolution
- Adapted projection operator technique for the treatment of initial correlations