Butterfly Echo Protocol for Axis-Agnostic Heisenberg-Limited Metrology

TL;DR

This paper introduces a novel echo-based protocol for axis-agnostic rotation sensing that uses chaotic dynamics to prepare random probe states, achieving Heisenberg-limited sensitivity without complex state preparation.

Contribution

It presents a new single-shot echo protocol utilizing chaotic dynamics for Heisenberg-limited, axis-agnostic rotation sensing, avoiding difficult anticoherent state preparation.

Findings

Achieves Heisenberg scaling for unknown rotation axes.

Uses constant-depth chaotic circuits for state preparation.

Sensitive to dephasing but feasible in near-term experiments.

Abstract

The extreme sensitivity of chaotic systems to external perturbations makes them natural candidates for sensing applications. We propose a single-shot echo-based protocol for estimating small rotations about an unknown axis that leverages random symmetric probe states prepared via chaotic dynamics. In contrast to previous protocols for this axis-agnostic rotation sensing problem that depend on difficult-to-prepare anticoherent states, the random probe states used in our protocol can be prepared via constant-depth chaotic circuits composed of random one-axis twisting pulses. We demonstrate analytically that our protocol achieves Heisenberg scaling relative to an arbitrary rotation axis that need not be a priori known. We also investigate the effects of collective and single-particle dephasing in our protocol using analytical and numerical tools. While the requirements on dephasing rates to maintain Heisenberg sensitivity are strict, they are achievable in near-term experiments, for instance, for magnetometric rotosensing with high-spin lanthanide atoms such as dysprosium-164.