Kraus representation for maps and master equation in spin star model with layered environment

TL;DR

This paper derives Kraus representations and master equations for a one-qubit system in a layered environment, revealing insights into the relation between CP maps and initial quantum correlations.

Contribution

It provides exact operator-sum and master equations for an exactly solvable spin star model with layered environment, including analysis of initial quantum correlations.

Findings

Exact Kraus and master equations derived for the model

Initial quantum correlation is not necessary for CP maps

Relation between CP maps and initial quantum correlations explored

Abstract

Quantum operations are usually defined as completely positive (CP), 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 an exactly solvable dynamic of one-qubit open system in layered environment . On the other hand, we obtain exact Nakajima-Zwanzig (NZ) and time-convolutionless (TCL) master equation from the maps. Finally, we study a simple example to consider the relation between CP maps and initial quantum correlation and show that vanishing initial quantum correlation is not necessary for CP maps.