Locally inequivalent four qubit hypergraph states

TL;DR

This paper classifies four-qubit hypergraph states into 28 inequivalent classes using symmetry and equivalence, confirming the minimal set with entanglement measures, which aids quantum code development.

Contribution

It provides a complete classification of four-qubit hypergraph states up to local equivalence, revealing the minimal set of such states for quantum information applications.

Findings

28 inequivalent hypergraph states identified

Symmetry and local equivalence reduce state complexity

Entanglement measures confirm minimal classification

Abstract

Hypergraph states as real equally weighted pure states are important resources for quantum codes of non-local stabilizer. Using local Pauli equivalence and permutational symmetry, we reduce the 32768 four qubit real equally weighted pure states to 28 locally inequivalent hypergraph states and several graph states. The calculation of geometric entanglement supplemented with entanglement entropy confirms that further reduction is impossible for true hypergraph states.