Bonn 2025 – wissenschaftliches Programm
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QI: Fachverband Quanteninformation
QI 9: Quantum Entanglement II
QI 9.2: Vortrag
Dienstag, 11. März 2025, 11:15–11:30, HS IX
Closed-Form Expressions for Two- and Three-Colorable States — •Konstantinos-Rafail Revis1,2, Hrachya Zakaryan1,2, and Zahra Raissi1,2 — 1Department of Computer Science, Paderborn University, Paderborn, Germany — 2Institute for Photonic Quantum Systems (PhoQS), Paderborn University, Paderborn, Germany
Graph states are a class of multi-partite entangled quantum states, where colorability, a property rooted in their mathematical foundation, has significant implications for quantum information processing. In this talk, we investigate the properties of graph states, focusing mainly on two-colorable and three-colorable graphs, but results for any colorability will be also discussed. A closed-form expression for all two-colorable graphs is presented. This result is tightly connected with the so-called orthogonal arrays and the minimum value of the Schmidt measure. Furthermore, we extend our analysis to every three-colorable graph state, revealing that they are equivalent via local operators to quantum orthogonal arrays, with a minimal number of Schmidt measure. The aforementioned results are extended to an arbitrary number of colors.
https://www.arxiv.org/abs/2408.09515
Keywords: Graph States; Qudits; Multipartite Entanglement; Schmidt Measure; (Quantum) Orthogonal Arrays