Entanglement of random hypergraph states

Abstract

Random quantum states and operations are of fundamental and practical interests. In this work, we investigate the entanglement properties of random hypergraph states, which generalize the notion of graph states by applying generalized controlled-phase gates on an initial reference product state. In particular, we study the two ensembles generated by random Controlled-Z(CZ) and Controlled-Controlled-Z(CCZ) gates, respectively. By applying tensor network representation and combinational counting, we analytically show that the average subsystem purity and entanglement entropy for the two ensembles feature the same volume law, but greatly differ in typicality, namely the purity fluctuation is small and universal for the CCZ ensemble while it is large for the CZ ensemble. We discuss the implications of these results for the onset of entanglement complexity and quantum chaos.

14+8 pages,9 figures,published version

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Cited by in corpus (7)

• Nonstabilizerness determining the hardness of direct fidelity estimation
• Magic of quantum hypergraph states
• Multipartite entanglement sudden death and birth in randomized hypergraph states
• Randomized hypergraph states and their entanglement properties
• Symmetry-Accelerated Classical Simulation of Clifford-Dominated Circuits
• Scattering entropies of quantum graphs with several channels
• Phase Transitions and Noise Robustness of Quantum Graph States