Entanglement, Quantum Correlators, and Connectivity in Graph States

This work presents a comprehensive exploration of the entanglement and graph connectivity properties of Graph States (GSs). Qubit entanglement in Pseudo Graph States (PGSs) is quantified using the Entanglement Distance (ED), a recently introduced measure of bipartite entanglement. In addition, a new approach is proposed for probing the underlying graph connectivity of genuine GSs, using Pauli matrix quantum correlators. These findings also reveal interesting implications for measurement processes, demonstrating the equivalence of some projective measurements. Finally, the emphasis is placed on the simplicity of data analysis in this framework. This work contributes to a deeper understanding of the entanglement and connectivity properties of GSs, offering valuable information for quantum information processing and quantum computing applications. The famous stabiliser formalism, which is the typically preferred framework for the study of this type of states, is not used in this work; on the contrary, this approach is based exclusively 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. This work explores entanglement and graph connectivity in graph states, a known universal resource for quantum computation. Quantifying qubit-wise entanglement with the novel entanglement distance for pseudo graph states, it introduces a method to probe genuine graph states' connectivity using quantum correlators of Pauli matrices. Unveiling equivalence in certain projective measurements, this approach, distinct from the stabilizer formalism, relies on intuitive tools like expectation values and quantum correlations. Offering insights into quantum information processing, it emphasizes simplicity in data analysis.image