Completely positive maps within the framework of direct-sum decomposition of state space

TL;DR

This paper characterizes initial states of open quantum systems that lead to completely positive reduced dynamics using direct-sum decomposition, including entangled states, and provides explicit Kraus operators.

Contribution

It introduces a comprehensive framework for identifying initial states resulting in CP maps, extending previous results to include entangled states.

Findings

Families of initial states include separable and entangled states.

Explicit Kraus operators are derived for these states.

The framework extends the understanding of reduced dynamics in open quantum systems.

Abstract

We investigate completely positive maps for an open system interacting with its environment. The families of the initial states for which the reduced dynamics can be described by a completely positive map are identified within the framework of direct-sum decomposition of state space. They includes not only separable states with vanishing or nonvanishing quantum discord but also entangled states. A general expression of the families as well as the Kraus operators for the completely positive maps are explicitly given. It significantly extends the previous results.