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QI: Fachverband Quanteninformation

QI 33: Quantum Materials and Many-Body Systems

QI 33.3: Talk

Friday, March 22, 2024, 10:00–10:15, HFT-TA 441

Closed-form expressions for graph states — •Hrachya Zakaryan, Konstantinos Rafail Revis, and Zahra Raissi — Department of Computer Science, Paderborn University, Germany

Two-colorable graphs states are multipartite entangled states, which can be represented by two-coloarble graphs. These are graphs where the vertices can be divided into two disjoint sets, such that no vertices in each set are connected by an edge. These graphs give rise to important graph states such as the cluster and GHZ states, which are vital quantum resources. We consider qudit systems, and therefore examine unweighted and weighted graphs, in two cases: Controlled-Z (CZ) edges and Controlled-Phase (CP) edges. Closed forms for their corresponding Local-Unitary (LU) equivalent states are obtained. Additionally, setups with specific phases and experimental interest, are examined. An extension of the stabilizer formalism to CP based graphs as well as multi-colorable graphs is considered.

Keywords: Graph states; Two-colorable graphs; Qudits; Multipartite entanglement