Local Pauli stabilizers of symmetric hypergraph states

TL;DR

This paper characterizes permutationally invariant hypergraph states with nontrivial local Pauli stabilizers, exploring their implications for quantum nonlocality and error correction, thus advancing understanding of complex entangled quantum states.

Contribution

It provides a complete characterization of symmetric hypergraph states with local Pauli stabilizers and discusses their applications in nonlocality and quantum error correction.

Findings

Identified conditions for nontrivial local Pauli stabilizers in symmetric hypergraph states

Connected stabilizer properties to nonlocality phenomena

Explored error correction capabilities of these states

Abstract

Hypergraph states of many quantum bits share the rich interplay between simple combinatorial description and nontrivial entanglement properties enjoyed by the graph states that they generalize. In this paper, we consider hypergraph states that are also permutationally invariant. We characterize the states in this class that have nontrivial local Pauli stabilizers and give applications to nonlocality and error correction.