Partial orbits of quantum gates and full three-particle entanglement

We introduce the notion of partial orbit for a given set of elementary quantum gates, and we study the action of different sets of gates on an initially three-particle disentangled state. We analyze the entanglement of the resulting quantum states by appealing to the violation of Svetlichny inequality. We find that the violation values are concentrated on specific regions. This constitutes evidence for the existence of a structure, which is quite different from that of a randomly generated (using the Haar measure) set of gates. In turn, this fact highlights the relevance of studying the physical properties of the partial orbits associated with different sets of elementary gates.

Automated summary

In this study, the notion of partial orbits for a given set of elementary quantum gates is introduced, and the entanglement of resulting quantum states is analyzed by the violation of Svetlichny inequality. It is found that the violation values are concentrated on specific regions, providing evidence for the existence of a structure distinct from randomly generated sets of gates. This emphasizes the importance of studying the physical properties of partial orbits associated with different sets of elementary gates.