Concurrence and three-tangle of the graph

A Joshi, R Singh, A Kumar - Quantum Information Processing, 2018 - Springer
A Joshi, R Singh, A Kumar
Quantum Information Processing, 2018Springer
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| 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 …
Abstract
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 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.
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