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Jordan, Thomas F.; Shaji, Anil; Sudarshan, E. C. G.

Dynamics of initially entangled open quantum systems. (English) Zbl 1227.82041

Phys. Rev. A (3) 70, No. 5, Part A, Article ID 052110, 14 p. (2004).
Summary: 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.

Cited in 36 Documents

MSC:

82C10 Quantum dynamics and nonequilibrium statistical mechanics (general)
81P15 Quantum measurement theory, state operations, state preparations
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References:

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