Synchronizing the Smallest Possible System

TL;DR

This paper explores the minimal quantum system size needed for synchronization, showing that spin 1 systems can synchronize with external signals while qubits cannot, using Husimi Q representations for analysis.

Contribution

It demonstrates that spin 1 systems can synchronize with external signals, unlike qubits, and introduces Husimi Q representation as a tool for phase portrait analysis.

Findings

Qubits cannot be synchronized due to lack of a limit cycle.

Spin 1 systems can be phase-locked to external signals.

Husimi Q representation effectively visualizes synchronization phenomena.

Abstract

We investigate the minimal Hilbert-space dimension for a system to be synchronized. We first show that qubits cannot be synchronized due to the lack of a limit cycle. Moving to larger spin values, we demonstrate that a single spin 1 can be phase-locked to a weak external signal of similar frequency and exhibits all the standard features of the theory of synchronization. Our findings rely on the Husimi Q representation based on spin coherent states which we propose as a tool to obtain a phase portrait.