Separability of Graph Laplacian Quantum States: Utilizing Unitary Operators, Neighbourhood Sets and Equivalence Relation

2024/01/04 by Anoopa Joshi, Joshi, Anoopa, Parvinder Singh +2
Computer Science · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Graph theory and applications #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2401.02289

openalex publication_date 2024/01/04 · openalex created_date 2024/01/07 · openalex updated_date 2026/07/28

Abstract

This article delves into an analysis of the intrinsic entanglement and separability feature in quantum states as depicted by graph Laplacian. We show that the presence or absence of edges in the graph plays a pivotal role in defining the entanglement or separability of these states. We propose a set of criteria for ascertaining the separability of quantum states comprising n-qubit within a composite Hilbert space, indicated as H=H₁ ⊗ H₂ ⊗ … ⊗ H_n. This determination is achieved through a combination of unitary operators, neighbourhood sets, and equivalence relations.

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