Qudit hypergraph states and their properties

Abstract

Hypergraph states, a generalization of graph states, constitute a large class of quantum states with intriguing non-local properties and have promising applications in quantum information science and technology. In this paper, we generalize hypergraph states to qudit hypergraph states, i.e., each vertex in the generalized hypergraph (multi-hypergraph) represents a $d$-level quantum system instead of a qubit. It is shown that multi-hypergraphs and $d$-level hypergraph states have a one-to-one correspondence. We prove that if one part of a multi-hypergraph is connected with the other part, the corresponding subsystems are entangled. More generally, the structure of a multi-hypergraph reveals the entanglement property of the corresponding quantum state. Furthermore, we discuss their relationship with some well-known state classes, e.g., real equally weighted states and stabilizer states. These states' responses to the generalized $Z$ ($X$) operations and $Z$ ($X$) measurements are studied. The Bell non-locality, an important resource in fulfilling many quantum information tasks, is also investigated.

12 pages, 5 figures

References in corpus (13)

• The Quantum Internet
• Multi-party entanglement in graph states
• Bell Inequalities for Graph States
• Quantum Error Correcting Codes Using Qudit Graph States
• All entangled pure states violate a single Bell's inequality
• Entanglement and nonclassical properties of hypergraph states
• Encoding Hypergraphs into Quantum States
• Non-adaptive Measurement-based Quantum Computation and Multi-party Bell Inequalities
• Local unitary symmetries of hypergraph states
• Qudit Hypergraph States
• Locally inequivalent four qubit hypergraph states
• Multipartite Entanglement and Hypergraph states of three qubits
• Entanglement of $\pi$-LME states and the SAT problem

Cited by in corpus (5)

• General framework for verifying pure quantum states in the adversarial scenario
• Efficient Verification of Hypergraph States
• Generalized cluster states from Hopf algebras: non-invertible symmetry and Hopf tensor network representation
• Entanglement of random hypergraph states
• Multipartite entanglement in qudit hypergraph states