Multipartite entanglement sudden death and birth in randomized hypergraph states

Abstract: We introduce and analyze the entanglement properties of randomized hypergraph states, as an extended notion of the randomization procedure in the quantum logic gates for the usual graph states, recently proposed in the literature. The probabilities of applying imperfect generalized controlled-$Z$ gates simulate the noisy operations over the qubits. We obtain entanglement measures as negativity, concurrence, and genuine multiparticle negativity, and show that entanglement exhibits a non-monotonic behavior in terms of the randomness parameters, which is a consequence of the non-uniformity of the associated hypergraphs, reinforcing the claim that the entanglement of randomized graph states is monotonic since they are related to $2$-uniform hypergraphs. Moreover, we observed the phenomena of entanglement sudden death and entanglement sudden birth in RH states. This work revels a connection between the non-uniformity of hypergraphs and loss of entanglement.