A Condition for the Nullity of Quantum Discord

TL;DR

This paper establishes a necessary and sufficient condition for zero quantum discord, linking it to strong subadditivity of von-Neumann entropy, and provides a mathematical definition of pointer states.

Contribution

It introduces a new criterion for null quantum discord states based on strong subadditivity, clarifying the structure of quantum correlations.

Findings

Zero quantum discord states are characterized by strong subadditivity.

Pointer states are mathematically defined as states with zero discord.

Strong subadditivity may define the boundary of quantum correlations.

Abstract

The positivity of quantum discord is shown to be equivalent to the strong subadditivity of von-Neumann entropy. This leads us to a necessary and sufficient condition characterizing the set of states with zero quantum discord. This also gives us a mathematical definition of pointer states, as they are the states with zero discord. Finally, we suggest that strong subadditivity of entropy might delineate the boundaries of the set of quantum correlations.