# Quantum discord of states arising from graphs

## TL;DR

This paper develops a graph-theoretic framework to characterize quantum discord in bipartite states, providing necessary and sufficient conditions for zero discord states based on graph properties.

## Contribution

It introduces a novel graph-theoretic approach to identify zero quantum discord states through properties of associated graphs and matrices.

## Key findings

- Graph properties reflect normality and commutativity of matrices related to quantum states.
- Graph measures for normality and commutativity are formulated.
- Classes of zero discord quantum states are identified using the graph-based criteria.

## Abstract

Quantum discord refers to an important aspect of quantum correlations for bipartite quantum systems. In our earlier works we have shown that corresponding to every graph (combinatorial) there are quantum states whose properties are reflected in the structure of the corresponding graph. Here, we attempt to develop a graph theoretic study of quantum discord that corresponds to a necessary and sufficient condition of zero quantum discord states which says that the blocks of density matrix corresponding to a zero quantum discord state are normal and commute with each other. These blocks have a one to one correspondence with some specific subgraphs of the graph which represents the quantum state. We obtain a number of graph theoretic properties representing normality and commutativity of a set of matrices which are indeed arising from the given graph. Utilizing these properties we define graph theoretic measures for normality and commutativity that results a formulation of graph theoretic quantum discord. We identify classes of quantum states with zero discord using the said formulation.