Abstract We investigate a family of quantum states defined by directed graphs,where the oriented edges represent interactions between ordered qubits. As a measureof entanglement, we adopt the Entanglement Distance—a quantity derived from theFubini–Study metric on the system’s projective Hilbert space.We demonstrate that this measure is entirely determined by the vertex degreedistribution and remains invariant under vertex relabeling, underscoring its topologicalnature. Consequently, the entanglement depends solely on the total degree of eachvertex, making it insensitive to the distinction between incoming and outgoing edges.These findings offer a geometric interpretation of quantum correlations andentanglement in complex systems, with promising implications for the design andanalysis of quantum networks.
Simone et al. (Thu,) studied this question.
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