Abstract
The constraints imposed by the initial system-environment correlation can lead to nonpositive Dynamical maps. We find the conditions for positivity and complete positivity of such dynamical maps by using the concept of an assignment map. Any initial system-environment correlations make the assignment map nonpositive, while the positivity of the dynamical map depends on the interplay between the assignment map and the system-environment coupling. We show how this interplay can reveal or hide the nonpositivity of the assignment map. We discuss the role of this interplay in Markovian models.
Highlights
The open quantum systems formalism is the standard tool used to understand and model the decoherence and thermalization of quantum systems
We find the conditions for positivity and complete positivity of such dynamical maps by using the concept of an assignment map
What we have shown in Eqs. (4) and (5) is that the positivity and complete positivity of the dynamical map are a function of the details of the composition of the assignment map and the unitary dynamics
Summary
Positivity in the presence of initial system-environment correlation. Rodrıguez-Rosario,3,4,† and Alan Aspuru-Guzik3 1Department of Physics, University of Oxford, Clarendon Laboratory, Oxford, United Kingdom. The constraints imposed by the initial system-environment correlation can lead to nonpositive dynamical maps. We find the conditions for positivity and complete positivity of such dynamical maps by using the concept of an assignment map. Any initial system-environment correlations make the assignment map nonpositive, while the positivity of the dynamical map depends on the interplay between the assignment map and the system-environment coupling. We show how this interplay can reveal or hide the nonpositivity of the assignment map. We discuss the role of this interplay in Markovian models
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