Emergent behaviours of a non-abelian quantum synchronisation model over the unitary group

Abstract

We introduce a new non-abelian quantum synchronisation model over the unitary group, represented as a gradient flow, where state matrices asymptotically converge to a common one up to phase translation. We provide a sufficient framework leading to quantum synchronisation based on Riccati-type differential inequalities. In addition, uniform time-delayed interaction is considered for modelling realistic communication, and we demonstrate that quantum synchronisation is persistent when a small time delay is allowed. Finally, numerical simulation is performed to visualise qualitative behaviours and support theoretical results.

Keywords

• Lohe model
• quantum synchronisation
• time delay
• unitary group
• 34C15
• 82C10
• 82C22