Universality of stochastic control of quantum chaos with measurement and feedback

TL;DR

This paper explores universal features of measurement-and-feedback control in quantum chaotic systems, revealing that quantum fluctuations set the transition's universality, independent of quantum interference effects.

Contribution

It introduces a universal control transition framework for quantum chaos, supported by quantum, semiclassical, and analytical models, highlighting the role of quantum fluctuations.

Findings

Universal control transition properties are set by quantum fluctuations.

Quantum signatures differ from classical limits, showing unique quantum effects.

The inverted harmonic oscillator effectively models quantum instability in control dynamics.

Abstract

We investigate universal features of measurement-and-feedback control of quantum chaotic dynamics by examining the quantum Arnold cat map, a paradigmatic model of quantum chaos. Inspired by probabilistic control of classical chaos, our protocol stochastically alternates between intrinsic instability and engineered control operations that steer trajectories toward a target point. Simulation of exact quantum dynamics and a semiclassical truncated Wigner approximation reveal universal properties of the cat map's control transition. To further characterize this universality, we introduce the inverted harmonic oscillator as an analytically tractable effective model of instability. By integrating numerical simulations, a semiclassical Fokker-Planck description, and a direct spectral analysis of the stochastic quantum channel, we identify quantum signatures absent in classical limits. The close agreement between quantum simulation, truncated Wigner approximation, and inverted oscillator analysis shows that universal features of the transition are set by uncertainty-limited quantum fluctuations and are insensitive to genuine quantum interference.