Quantifying Quantum Entanglement in Two-Qubit Mixed State from Connected Correlator

TL;DR

This paper introduces a connected correlation matrix approach to quantify quantum entanglement in two-qubit mixed states, demonstrating its effectiveness and potential for local interpretation of entanglement.

Contribution

The study proposes using connected correlation as a new measure for quantum entanglement, linking it to entanglement degree and local observability.

Findings

Connected correlation increases monotonically with entanglement.

Separable states show minimal connected correlation.

Connected correlation effectively quantifies entanglement.

Abstract

Our study employs a connected correlation matrix to quantify Quantum Entanglement. The matrix encompasses all necessary measures for assessing the degree of entanglement between particles. We begin with a three-qubit state and involve obtaining a mixed state by performing partial tracing over one qubit. Our goal is to exclude the non-connected sector by focusing on the connected correlation. This suggests that the connected correlation is deemed crucial for capturing relevant entanglement degrees. The study classifies mixed states and observes that separable states exhibit the lowest correlation within each class. We demonstrate that the entanglement measure monotonically increases concerning the correlation measure. This implies that connected correlation serves as an effective measure of Quantum Entanglement. Finally, our proposal suggests that interpreting Quantum Entanglement from a local perspective is possible. The observable is described as a vector with locality but violates freedom of choice.