Structure of correlated initial states that guarantee completely positive reduced dynamics

Abstract

We use the Koashi-Imoto decomposition of the degrees of freedom of joint system-environment initial states to investigate the reduced dynamics. We show that a subset of joint system-environment initial states guarantees completely positive reduced dynamics, if and only if the system privately owns all quantum degrees of freedom and can locally access the classical degrees of freedom, without disturbing all joint initial states in the given subset. Furthermore, we show that the quantum mutual information for such kinds of states must be independent of the quantum degrees of freedom.

5 pages, 1 figure. Accepted version. To appear in Physical Review A

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Cited by in corpus (10)

• On the dynamics of initially correlated open quantum systems: theory and applications
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• Causal classification of spatiotemporal quantum correlations
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• When the assignment map is completely positive
• Structure of states for which each localized dynamics reduces to a localized subdynamics
• Positivity of the assignment map implies complete positivity of the reduced dynamics
• Requiring linearity leads to complete positivity
• Complete positivity on the subsystems level