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QI: Fachverband Quanteninformation
QI 9: Quantum Entanglement II
QI 9.5: Vortrag
Dienstag, 11. März 2025, 12:00–12:15, HS IX
Non-symmetric GHZ states; weighted hypergraph and controlled-unitary graph representations — •Hrachya Zakaryan1,2, Konstantinos-Rafail Revis1,2, and Zahra Raissi1,2 — 1Department of Computer Science, Paderborn University, Paderborn, Germany — 2Institute for Photonic Quantum Systems (PhoQS), Paderborn University, Paderborn, Germany
Non-symmetric GHZ states, represent a significant yet underexplored class of multipartite entangled states with potential applications in quantum information. Despite their importance, the lack of a well-defined stabilizer formalism and corresponding graph representation has hindered their comprehensive study. We address this gap by introducing two novel graph formalisms and stabilizers for non-symmetric GHZ states. We provide a weighted hypergraph representation and demonstrate that non-symmetric GHZ states are local unitary (LU) equivalent to fully connected weighted hypergraphs. We provide stabilizers using local operations, and an ancilla. We further extend this framework to qudits, offering a specific form for non-symmetric qudit GHZ states and their LU equivalent weighted qudit hypergraphs. Lastly, we propose a graph formalism using controlled-unitary (CU) operations, showing that non-symmetric qudit GHZ states can be described using star-shaped CU graphs.
https://arxiv.org/abs/2408.02740
Keywords: Graph States; Hypergraph States; Multipartite Entanglement; GHZ States; Qudits