Bipartite entanglement and hypergraph states

TL;DR

This paper explores multipartite entanglement in hypergraph states using hypergraph theory, introduces a method to compute concurrence between qubits, and characterizes bipartite entanglement in specific hypergraph states.

Contribution

It presents a hypergraph-theoretic approach to quantify bipartite entanglement in hypergraph states and characterizes entanglement properties of special hypergraph states.

Findings

A graph component with vertices {i,j} indicates entanglement between qubits i and j.

Each qubit pair in a certain hypergraph state is entangled similarly to a generalized W state.

The proposed method effectively computes concurrence using Hamming weights of subhypergraphs.

Abstract

We investigate some properties of multipartite entanglement of hypergraph states in purely hypergraph theoretical terms. We first introduce an approach for computing the concurrence between two specific qubits of a hypergraph state by using the so-called Hamming weights of several special subhypergraphs of the corresponding hypergraph. Then we quantify and characterize bipartite entanglement between each qubit pair of several special hypergraph states in terms of the concurrence obtained by using the above approach. Our main results include that (i) a graph g has a component with the vertex set {i,j} if and only if the qubit pair labeled by {i,j} of the graph state |g> is entangled; and (ii) each qubit pair of a special hypergraph state is entangled like the generalized W state.