Entanglement in eight-qubit graph states

TL;DR

This paper classifies eight-qubit graph states into equivalence classes, identifying minimal gate representations and calculating entanglement measures, thereby extending previous classifications to more complex quantum systems.

Contribution

It extends the classification of graph states to eight qubits, providing minimal gate representations and entanglement measures for each class.

Findings

Identified 101 equivalence classes of 8-qubit graph states.

Determined minimal controlled-Z gate representations for each class.

Calculated Schmidt measures and ranks for entanglement analysis.

Abstract

Any 8-qubit graph state belongs to one of the 101 equivalence classes under local unitary operations within the Clifford group. For each of these classes we obtain a representative which requires the minimum number of controlled-Z gates for its preparation, and calculate the Schmidt measure for the 8-partite split, and the Schmidt ranks for all bipartite splits. This results into an extension to 8 qubits of the classification of graph states proposed by Hein, Eisert, and Briegel [Phys. Rev. A 69, 062311 (2004)].