Butterfly Echo Protocol for Axis-Agnostic Heisenberg-Limited Metrology

• URL: http://arxiv.org/abs/2602.23332v1
• Date: Thu, 26 Feb 2026 18:38:01 GMT
• Title: Butterfly Echo Protocol for Axis-Agnostic Heisenberg-Limited Metrology
• Authors: Jacob Bringewatt, Leon Zaporski, Matthew Radzihovsky, Jasmine Albert, Alexey V. Gorshkov, Vladan Vuletic, Gregory Bentsen,
• Abstract summary: We propose a single-shot echo-based protocol for estimating small rotations about an unknown axis.<n>We demonstrate analytically that our protocol achieves Heisenberg scaling relative to an arbitrary rotation axis.<n>While the requirements on dephasing rates to maintain Heisenberg sensitivity are strict, they are achievable in near-term experiments.
• Score: 0.039089069256361735
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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