Local Pauli stabilizers of symmetric hypergraph states
David W Lyons, Nathaniel P Gibbons, Mark A Peters, Daniel J Upchurch, Scott N Walck, Ezekiel W Wertz · Journal of Physics A Mathematical and Theoretical · 2017
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.