Entropic measure and hypergraph states

TL;DR

This paper explores the entanglement properties of hypergraph states using hypergraph theory, introducing a method to compute local entropic measures and revealing that some hypergraph states cannot be transformed into graph states via local unitaries.

Contribution

It presents a hypergraph-theoretic approach to quantify entanglement in hypergraph states and characterizes their convertibility to graph states.

Findings

A method to compute local entropic measures using t-adjacent subhypergraphs.

Hypergraph states with certain properties cannot be converted into graph states.

Provides a hypergraph-based characterization of entanglement in quantum states.

Abstract

We investigate some properties of the entanglement of hypergraph states in purely hypergraph theoretical terms. We first introduce an approach for computing local entropic measure on qubit t of a hypergraph state by using the Hamming weight of the so-called t-adjacent subhypergraph. Then we quantify and characterize the entanglement of hypergraph states in terms of local entropic measures obtained by using the above approach. Our results show that a class of n-qubit hypergraph states can not be converted into any graph state under local unitary transformations.