Phys. Rev. A 70, 052110 (2004) - Dynamics of initially entangled open quantum systems

Dynamics of initially entangled open quantum systems

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

Phys. Rev. A 70, 052110 – Published 19 November 2004

Abstract

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.

Received 12 June 2004

DOI:https://doi.org/10.1103/PhysRevA.70.052110

©2004 American Physical Society

Authors & Affiliations

Thomas F. Jordan^*

Physics Department, University of Minnesota, Duluth, Minnesota 55812, USA

The University of Texas at Austin, Center for Statistical Mechanics, 1 University Station C1609, Austin, Texas 78712, USA

E. C. G. Sudarshan^‡

The University of Texas at Austin, Center for Particle Physics, 1 University Station C1602, Austin, Texas 78712, USA

^*Electronic address: tjordan@d.umn.edu
^†Electronic address: shaji@physics.utexas.edu
^‡Electronic address: sudarshan@physics.utexas.edu

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Vol. 70, Iss. 5 — November 2004

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