Vanishing quantum discord is necessary and sufficient for completely positive maps

TL;DR

This paper proves that completely positive quantum maps correspond exactly to initial states with zero quantum discord, resolving longstanding questions about the conditions for quantum dynamics to be represented by such maps.

Contribution

It establishes that vanishing quantum discord is both necessary and sufficient for the emergence of completely positive maps from initial system-bath states.

Findings

CP maps originate only from states with zero quantum discord

All initial states lead to Hermitian maps

The results settle two fundamental open problems in quantum theory

Abstract

Two long standing open problems in quantum theory are to characterize the class of initial system-bath states for which quantum dynamics is equivalent to (1) a map between the initial and final system states, and (2) a completely positive (CP) map. The CP map problem is especially important, due to the widespread use of such maps in quantum information processing and open quantum systems theory. Here we settle both these questions by showing that the answer to the first is "all", with the resulting map being Hermitian, and that the answer to the second is that CP maps arise exclusively from the class of separable states with vanishing quantum discord.