Entanglement, Quantum Correlators, and Connectivity in Graph States

Year: 2024

Authors: Vesperini A., Franzosi R.

Autors Affiliation: Univ Siena, DSFTA, Via Roma 56, I-53100 Siena, Italy; Aix Marseille Univ, Ctr Phys Theor, Campus Luminy,Case 907, F-13288 Marseille 09, France; Ist Nazl Ottica, QSTAR, Largo Enrico Fermi 2, I-50125 Florence, Italy; Ist Nazl Ottica, CNR, Largo Enrico Fermi 2, I-50125 Florence, Italy; INFN Sez Perugia, I-06123 Perugia, Italy.

Abstract: 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

Journal/Review: ADVANCED QUANTUM TECHNOLOGIES

Volume: 7 (2)      Pages from:   to:

More Information: The authors acknowledged support from the RESEARCH SUPPORT PLAN 2022 – Call for applications for funding allocation to research projects curiosity driven (F CUR) – Project Entanglement Protection of Qubits’ Dynamics in a Cavity – EPQDC, and the support by the Italian National Group of Mathematical Physics (GNFM-INdAM).
KeyWords: connectivity; entanglement; graph state; measurement-based quantum computation; projective measurement; quantum correlator; quantum information
DOI: 10.1002/qute.202300264

Citations: 2
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