Randomized hypergraph states and their entanglement properties

Abstract: We study the entanglement properties of randomized hypergraph states, extending the concept of randomized graph states to encompass hypergraph-based quantum states. In our model, imperfect generalized multiqubit gates are applied probabilistically, simulating experimentally realistic noisy gate operations where gate fidelity decreases with increasing hyperedge order. We analyze bipartite and genuine multipartite entanglement of these mixed multiqubit states. Numerical results for various hypergraph configurations up to four qubits reveal rich and sometimes nonmonotonic entanglement behavior, stemming from the interplay between hyperedge structure and gate imperfections. We derive analytical expressions for entanglement witnesses based on randomization overlap for new hypergraph families. Our findings contribute to the understanding of entanglement resilience under gate imperfections, providing insights for the experimental implementation of hypergraph states in noisy quantum devices.