Synchronizing the simplest classical system and then quantizing it

Abstract

We propose a discrete synchronization model of a finite d-level system and discuss what happens once superposition of states is allowed. The model exhibits various asymptotic behaviors that depend on the initial state. In particular, two antagonistic phenomena can occur: A transition into a product of two basis states and an entanglement generation. Next, we generalize this model and show that it is possible to phase lock a periodic dynamics of a single qubit to a periodic dynamics of a single qudit. Finally, we present a spin system whose dynamics is a continuous-time analog of the above discrete model.