Super-Heisenberg Scaling Using Nonlinear Quantum Scrambling

TL;DR

This paper demonstrates that nonlinear quantum scrambling enables super-Heisenberg scaling in quantum metrology, even in dissipative systems, by leveraging nonlinear resources and squeezing techniques for enhanced measurement precision.

Contribution

It introduces a novel approach using nonlinear quantum scrambling to achieve super-Heisenberg scaling with time-independent generators, including in dissipative systems.

Findings

Super-Heisenberg scaling achieved via nonlinear quantum scrambling.

Enhanced measurement precision with injected and intracavity squeezing.

Superior scaling in dissipative optical cavity systems.

Abstract

Super-Heisenberg scaling, which scales as $N^{-\beta}$ with $\beta>1$ in terms of the number of particles $N$ or $T^{-\beta}$ in terms of the evolution time $T$, is better than Heisenberg scaling in quantum metrology. It has been proven that super-Heisenberg scaling can be achieved when the Hamiltonian of the system involves many-body interactions or the time-dependent terms. We demonstrate that nonlinear quantum scrambling facilitates the achievement of super-Heisenberg scaling $T^{-\beta}$ when the generator of the parameter is time-independent. More importantly, in dissipative systems, we can still obtain super-Heisenberg scaling in the friction model. In the optical cavity system, an exponential improvement in measurement precision over time can be achieved by combining injected external squeezing and intracavity squeezing. Our work provides an optimal method for leveraging nonlinear resources to enhance the measurement precision of the driving field.