Dynamics of initially entangled open quantum systems
By Thomas F. Jordan, Anil Shaji, E. Sudarshan. 2004
174 citations recorded by the source corpus.
Linear maps of matrices describing the evolution of density matrices for a quantum system initially entangled with another are identified and found to be not always completely positive. They can even map a positive matrix to a matrix that is not positive, unless we restrict the domain on which the map acts. Nevertheless, their form is similar to that of completely positive maps. Only some minus signs are inserted in the operator-sum representation. Each map is the difference of two completely positive maps. The maps are first obtained as maps of mean values and then as maps of basis matrices. These forms also prove to be useful. An example for two entangled qubits is worked out in detail. The relation to earlier work is discussed.
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/67fcdda58c3cc3ac0ab1b07c6a3fcde1f2bc108c
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In Artificial Intelligence
In Atomic and Molecular Physics, and Optics
In Statistical and Nonlinear Physics
Citations in the corpus
- Dynamics of non-Markovian open quantum systems (2015, background): “In this regard, it was shown by Carteret et al. (2008) and Jordan et al. (2004) that assignment maps producing certain entangled initial system-bath 13 states may indeed lead to non-CP dynamics.”
- Completely positive maps and classical correlations (2007, background): “Since we know that entanglement in ρSE typically leads to not completely positive dynamics for S [12], we first look to see if separability of the initial state is sufficient to guarantee complete positivity.”