Concurrence and three-tangle of the graph

In this article, we study the entanglement properties of two-qubit quantum states based on concurrence using the graph-theoretic approach. Entanglement properties of a density operator are obtained from the combinatorial Laplacian matrix which is constructed for a given graph. In the study of entang...

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Bibliographic Details
Published in:Quantum information processing 2018-12, Vol.17 (12), p.1-31, Article 327
Main Authors: Joshi, Anoopa, Singh, Ranveer, Kumar, Atul
Format: Article
Language:English
Subjects:
Combinatorial analysis
Data Structures and Information Theory
Graph theory
Mathematical Physics
Physics
Physics and Astronomy
Quantum Computing
Quantum entanglement
Quantum Information Technology
Quantum Physics
Quantum theory
Qubits (quantum computing)
Spintronics
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Summary:In this article, we study the entanglement properties of two-qubit quantum states based on concurrence using the graph-theoretic approach. Entanglement properties of a density operator are obtained from the combinatorial Laplacian matrix which is constructed for a given graph. In the study of entanglement, we found that measure of entanglement is either 1 | E | or zero for simple graphs. We further propose a simple method to evaluate the three-tangle and analyze inequivalent classes belonging to three-qubit pure states using graph-theoretic perspective. Our results allow a clear distinction between three-qubit separable states, genuinely entangled Greenberger–Horne–Zeilinger and W states, purely based on graphical interpretations.
ISSN:1570-0755
1573-1332
DOI:10.1007/s11128-018-2085-5