Structure of correlated initial states that guarantee completely positive reduced dynamics

TL;DR

This paper characterizes the initial states of a system and environment that ensure the reduced dynamics are completely positive, using the Koashi-Imoto decomposition to identify the necessary quantum and classical degrees of freedom.

Contribution

It provides a necessary and sufficient condition for initial states to guarantee completely positive reduced dynamics based on their quantum and classical structure.

Findings

States with all quantum degrees of freedom privately owned by the system ensure CP dynamics

Classical degrees of freedom accessible locally by the system are essential

Quantum mutual information must be independent of quantum degrees of freedom for such states

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.