Time-reversal-based quantum metrology in a central-spin architecture: from SATIN to butterfly echo
Abstract
We investigate quantum-enhanced time-reversal-based metrology using the central spin model, in which a single ancilla spin of magnitude Scen mediates interactions between N bath spins through a star-graph topology. We demonstrate that the SATIN (Signal Amplification Through Time-reversal Interaction) echo protocol can be implemented in this setup to achieve a Fisher information of N2/e with the collective ⟨ Jy⟩ readout, corresponding to a 4.34 dB offset from the Heisenberg limit. Furthermore, we establish that this platform provides a pathway to perform the butterfly echo protocol by conjugating each evolution step with a random collective bath rotation, thereby achieving axis-agnostic Heisenberg-scaled sensing. Crucially, with a small N−independent number of random steps, the butterfly echo reaches a Fisher information of N2/4 (6 dB below the Heisenberg limit) for any unknown encoding axis, with the plateau gain tracking the Haar limit. Finally, we demonstrate that the central-spin magnitude Scen provides a powerful knob to reduce the optimal protocol timescale without altering the metrological ceiling or the circuit depth required to reach isotropy. The proposed scheme is relevant to cavity QED and NMR quantum processors, where the central spin architecture arises naturally.
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BibTeX
@misc{kumar2026timereversalbased,
title = {{Time-reversal-based quantum metrology in a central-spin architecture: from SATIN to butterfly echo}},
author = {Aditya Kumar and Sayan Choudhury},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30686},
eprint = {2610.30686},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30686},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Time-reversal-based quantum metrology in a central-spin architecture: from SATIN to butterfly echo
AU - Aditya Kumar
AU - Sayan Choudhury
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.30686
UR - https://arxiv.org/abs/2610.30686
AB - We investigate quantum-enhanced time-reversal-based metrology using the central spin model, in which a single ancilla spin of magnitude S_cen mediates interactions between N bath spins through a star-graph topology. We demonstrate that the SATIN (Signal Amplification Through Time-reversal Interaction) echo protocol can be implemented in this setup to achieve a Fisher information of N^2/e with the collective ⟨ J_y⟩ readout, corresponding to a 4.34 dB offset from the Heisenberg limit. Furthermore, we establish that this platform provides a pathway to perform the butterfly echo protocol by conjugating each evolution step with a random collective bath rotation, thereby achieving axis-agnostic Heisenberg-scaled sensing. Crucially, with a small N−independent number of random steps, the butterfly echo reaches a Fisher information of N^2/4 (6 dB below the Heisenberg limit) for any unknown encoding axis, with the plateau gain tracking the Haar limit. Finally, we demonstrate that the central-spin magnitude S_cen provides a powerful knob to reduce the optimal protocol timescale without altering the metrological ceiling or the circuit depth required to reach isotropy. The proposed scheme is relevant to cavity QED and NMR quantum processors, where the central spin architecture arises naturally.
ER -