Entanglement, quantum correlators and connectivity in graph states

TL;DR

This paper investigates the entanglement and connectivity of graph states using quantum correlators and entanglement measures, providing new insights without relying on stabilizer formalism, thus enhancing understanding for quantum information processing.

Contribution

It introduces a novel approach to analyze graph state connectivity and entanglement using expectation values and quantum correlations, avoiding stabilizer formalism.

Findings

Quantifies entanglement in pseudo graph states with entanglement distance

Proposes a new method to probe graph connectivity via quantum correlators

Shows implications for measurement processes and data analysis simplicity

Abstract

In this work, we present a comprehensive exploration of the entanglement and graph connectivity properties of graph states. We quantify the entanglement in pseudo graph states using the entanglement distance, a recently introduced measure of entanglement. Additionally, we propose a novel approach to probe the underlying graph connectivity of genuine graph states, using quantum correlators of Pauli matrices. Our findings also reveal interesting implications for measurement processes, demonstrating the equivalence of certain projective measurements. Finally, we emphasize the simplicity of data analysis within this framework. This work contributes to a deeper understanding of the entanglement and connectivity properties of graph states, offering valuable insights for quantum information processing and quantum computing applications. In this work, we do not resort to the celebrated stabilizer formalism, which is the framework typically preferred for the study of this type of state; on the contrary, our approach is solely based on the concepts of expectation values, quantum correlations and projective measurement, which have the advantage of being very intuitive and fundamental tools of quantum theory.