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Nakajima-Zwanzig and Time-Convolutionless Master Equations for a One-Qubit System in a Non-Markovian Layered Environment

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Abstract

Quantum operations, are completely positive (CP) and trace preserving (TP) maps on quantum states, and can be represented by operator-sum or Kraus representations. In this paper, we calculate operator-sum representation and master equation of one-qubit open quantum system in layered environment which is a generalized spin star model. The Nakajima-Zwanzig and time-convolutionless projection operators technique are applied for deriving the master equations. Finally, a simple example will be studied to consider the relation between completely positive maps and initial quantum correlation and show that vanishing quantum discord is not necessary for CP maps.

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  1. Department of Theoretical Physics and Astrophysics, University of Tabriz, Tabriz, 51664, Iran

    M. Mahdian & H. Mehrabpour

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  1. M. Mahdian
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  2. H. Mehrabpour
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Correspondence to M. Mahdian.

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Mahdian, M., Mehrabpour, H. Nakajima-Zwanzig and Time-Convolutionless Master Equations for a One-Qubit System in a Non-Markovian Layered Environment. Int J Theor Phys 53, 2785–2795 (2014). https://doi.org/10.1007/s10773-014-2075-z

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