Complete positivity of a spin-12 master equation with memory

Sabrina Maniscalco
Phys. Rev. A 75, 062103 – Published 6 June 2007

Abstract

We study a non-Markovian spin-12 master equation with exponential memory. We derive the conditions under which the dynamical map describing the reduced system dynamics is completely positive, i.e., the nonunitary evolution of the system is compatible with a description in terms of a closed total spin-reservoir system. Our results show that for a zero-T reservoir, the dynamical map of the model here considered is never completely positive. For moderate- and high-T reservoirs, on the contrary, positivity is a necessary and sufficient condition for complete positivity. We also consider the Shabani-Lidar master equation recently introduced [A. Shabani and D.A. Lidar, Phys. Rev. A 71, 020101(R) (2005)] and we demonstrate that such a master equation is always completely positive.

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  • Received 22 March 2006

DOI:https://doi.org/10.1103/PhysRevA.75.062103

©2007 American Physical Society

Authors & Affiliations

Sabrina Maniscalco*

  • Department of Physics, University of Turku, FIN-20014, Turun yliopisto, Turun Yliopisto, Finland

  • *Electronic address: sabrina.maniscalco@utu.fi

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Issue

Vol. 75, Iss. 6 — June 2007

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