Entanglement and nonclassical properties of hypergraph states

TL;DR

This paper investigates the entanglement and nonclassical properties of hypergraph states, providing classifications, conditions for local unitary equivalence, and demonstrating their potential to reveal quantum nonlocality and contextuality.

Contribution

It offers a systematic classification of hypergraph states up to six qubits, establishes criteria for local unitary equivalence, and derives nonlocality inequalities for these states.

Findings

Classified hypergraph states for up to six qubits.

Established criteria for local unitary equivalence.

Derived nonlocality and contextuality inequalities.

Abstract

Hypergraph states are multi-qubit states that form a subset of the locally maximally entangleable states and a generalization of the well--established notion of graph states. Mathematically, they can conveniently be described by a hypergraph that indicates a possible generation procedure of these states; alternatively, they can also be phrased in terms of a non-local stabilizer formalism. In this paper, we explore the entanglement properties and nonclassical features of hypergraph states. First, we identify the equivalence classes under local unitary transformations for up to four qubits, as well as important classes of five- and six-qubit states, and determine various entanglement properties of these classes. Second, we present general conditions under which the local unitary equivalence of hypergraph states can simply be decided by considering a finite set of transformations with a clear graph-theoretical interpretation. Finally, we consider the question whether hypergraph states and their correlations can be used to reveal contradictions with classical hidden variable theories. We demonstrate that various noncontextuality inequalities and Bell inequalities can be derived for hypergraph states.