Vanishing quantum discord is not necessary for completely-positive maps

TL;DR

This paper demonstrates that vanishing quantum discord is not a necessary condition for the dynamics of a quantum system to be described by completely-positive maps, challenging previous assumptions in quantum information theory.

Contribution

It provides a counterexample showing non-zero quantum discord can still result in completely-positive maps, clarifying the relationship between discord and quantum dynamics.

Findings

Counterexample with non-zero discord and CP map

Challenges previous claim on discord's necessity for CP maps

Discussion on physical validity of different initial state assumptions

Abstract

The description of the dynamics of a system that may be correlated with its environment is only meaningful within the context of a specific framework. Different frameworks rely upon different assumptions about the initial system-environment state. We reexamine the connections between complete-positivity and quantum discord within two different sets of assumptions about the relevant family of initial states. We present an example of a system-environment state with non-vanishing quantum discord that leads to a completely-positive map. This invalidates an earlier claim on the necessity of vanishing quantum discord for completely-positive maps. In our final remarks we discuss the physical validity of each approach.