Abstract
I propose a discrete synchronization model of finite d-level systems 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 quantum-to-classical transition and entanglement generation. Next, I 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 qudit stimulus.
Highlights
Synchronization is a process in which two or more interacting oscillators adjust their rhythms
Let us first consider a case in which the stimulus is prepared in one of the basis states, whereas the oscillator is prepared in a superposition
We considered a discrete version of the PPO synchronization model and showed that the smallest classical system that can be synchronized is a single bit
Summary
Synchronization is a process in which two or more interacting oscillators adjust their rhythms. This work stimulated further research [5,6,7,8] and, at the moment, there are arguments for [8] and against [5] single spin-1/2 synchronization These contrary arguments originate from a problem of how to define a limit cycle in quantum dynamics. The goal of this work is to use the above PPO analogy to derive a quantum synchronization model of an arbitrary spin-s system or, more generally, a qudit. Our main motivation behind this approach comes from the fact that qudits are discrete-state systems Both a classical d-level system and a qudit can store the same amount of classical information. We are going to discretize the PPO synchronization model We quantize it and focus on dynamics in which superposed initial states are allowed. At the end, we are going to show that there is some parallel between this model and an open continuous-time spin dynamics
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