# Detecting Two Qubit Both-Way Positive Discord States

## TL;DR

This paper presents an analytical method to detect two-qubit states with both-way non-zero quantum discord, providing necessary and sufficient conditions that consider correlation tensors and local Bloch vectors.

## Contribution

It introduces a set of exact conditions for identifying two-qubit states with positive quantum discord in both directions, advancing understanding of quantum correlations beyond entanglement.

## Key findings

- Derived necessary and sufficient conditions for both-way non-zero discord
- Identified the role of correlation tensor and local Bloch vectors in detection
- Provided analytical framework for classifying classical-quantum and quantum-classical states

## Abstract

Quantum discord plays a pragmatic role in analyzing nonclassical feature of quantum correlations beyond entanglement. It is used in several information processing protocols which lacks sufficient amount of entanglement to be used as a resource. We have provided with an analytical method of detecting quantum discord of an arbitrary two qubit state. We have formulated a set of necessary and sufficient conditions for any two qubit state to be a both-way non-zero quantum discord state. As quantum discord is asymmetric in nature, we have framed the set of if and only if conditions for a two qubit state to be classical-quantum as well for it to be quantum-classical. Interestingly, not only correlation tensor but also local Bloch vector(corresponding to the classical party) plays a role for detecting the state to be a positive discord state.