Randomized hypergraph states and their entanglement properties

TL;DR

This paper investigates the entanglement properties of randomized hypergraph states under noisy gate operations, providing analytical tools and numerical insights relevant for quantum experiments.

Contribution

It extends the concept of randomized mixed graph states to hypergraph states, analyzing their entanglement under realistic noisy conditions and deriving new entanglement witnesses.

Findings

Entanglement behavior is rich and sometimes nonmonotonic depending on hypergraph structure.

Analytical expressions for entanglement witnesses are derived for new hypergraph families.

Numerical results show entanglement resilience varies with hyperedge configuration and noise.

Abstract

We study the entanglement properties of randomized mixed hypergraph states, extending the concept of randomized mixed graph states to encompass hypergraph-based quantum states. In our model, imperfect generalized multi-qubit 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 multi-qubit states. Numerical results for various hypergraph configurations with up to four qubits reveal rich, 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 understanding entanglement resilience under gate imperfections, providing insight into the experimental implementation of hypergraph states in noisy quantum devices.