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Optical and Quantum Sensing and Precision Metrology II

Brownian spin dynamics for axis-agnostic precision metrology

Jasmine Albert, Gregory S. Bentsen

Published Mar 5, 2026• 0 citations
Publisher

Abstract

Anticoherent states are known to enable Heisenberg-limited precision measurements of external fields B→ = Bnˆ along arbitrary, apriori unknown rotation axes ˆn. In this paper we propose efficient protocols for producing approximate anticoherent states using random circuit dynamics acting on a single large spin S→. In particular, we propose two circuit models (Brownian and Random One-Axis Twist) to efficiently generate anticoherent spin states. Using the Choi-Jamio lkowski isomorphism (channel-state duality), we demonstrate that the behavior of these two models is identical given sufficiently short twisting times, and that these models can reach approximate anticoherence in constant circuit depth in the large-S limit.

DOI
10.1117/12.3089694

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Anticoherent states are known to enable Heisenberg-limited precision measurements of external fields B→ = Bnˆ along arbitrary, apriori unknown rotation axes ˆn. In this paper we propose efficient protocols for producing approximate anticoherent states using random circuit dynamics acting on a single large spin S→. In particular, we propose two circuit models (Brownian and Random One-Axis Twist) to efficiently generate anticoherent spin states. Using the Choi-Jamio lkowski isomorphism (channel-state duality), we demonstrate that the behavior of these two models is identical given sufficiently short twisting times, and that these models can reach approximate anticoherence in constant circuit depth in the large-S limit.
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. Further, the signal of interest can be extracted simply by measuring the total spin polarization. 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, in magnetometric rotosensing with high-spin lanthanide atoms such as dysprosium-164.
Quantum metrology and sensing seek advantages in estimating an unknown parameter of some quantum state or channel, using entanglement such as spin squeezing produced by one-axis twists or other quantum resources. In particular, qubit phase estimation, or rotation sensing, appears as a ubiquitous problem with applications to electric field sensing, magnetometry, atomic clocks, and gyroscopes. By adopting the Bayesian formalism to the phase estimation problem to account for limited initial knowledge about the value of the phase, we formulate variational metrology and treat the state preparation (or encoding) and measurement (or decoding) procedures as parameterized quantum circuits. It is important to understand how effective various parametrized protocols are as well as how robust they are to the effects of complex noise such as spatially correlated noise. First, we propose a family of parametrized encoding and decoding protocols called arbitrary-axis twist ansatzes, and show that it can lead to a substantial reduction in the number of one-axis twists needed to achieve a target estimation error. Furthermore, we demonstrate that the estimation error associated with these strategies decreases with system size in a faster manner than classical (or no-twist) protocols, even in the less-explored regimes where the prior information is limited. Last, using a polynomial-sized tensor network algorithm, we numerically analyze practical variational metrology beyond the symmetric subspace of a collective spin and find that quantum advantage persists for the arbitrary-axis twist ansatzes with a few one-axis twists and smaller total twisting angles for practically relevant noise levels. Published by the American Physical Society 2024
One core of quantum metrology is the utilization of entanglement to enhance measurement precision beyond the standard quantum limit. Here, we utilize the Floquet-engineered two-axis twisting (TAT) and turn dynamics to generate GHZ-like states for quantum metrology. Using both analytical semi-classical and quantum approaches, we find that the desired NNN-particle GHZ-like state can be produced in a remarkably short time topt∝ln⁡N/Nt_\mathrm{opt}\propto \ln{N}/{N}topt​∝lnN/N, and its quantum Fisher information FQopt∝N2F^\mathrm{opt}_\mathrm{Q}\propto N^2FQopt​∝N2 approaches the Heisenberg limit. Owing to the rapid state preparation, it shows outstanding robustness against decoherence. Moreover, using the Floquet-engineered anti-TAT-and-turn, one may implement an efficient interaction-based readout protocol to extract the signal encoded in this GHZ-like state. This Floquet-engineered anti-TAT-and-turn approach offers a viable method to achieve effective time-reversal dynamics to improve measurement precision and resilience against detection noise, all without the need to invert the sign of the nonlinear interaction. This study paves a way for achieving entanglement-enhanced quantum metrology via rapid generation of GHZ-like states at high particle numbers through continuous Floquet engineering.
Phase estimation with potentially large phase values, i.e., with large dynamic range, has many applications in quantum metrology, for example to atomic clocks. A recently proposed phase estimation scheme approaches the Heisenberg scaling in this global setting using sequences of increasingly squeezed Gaussian states as probes and adaptively chosen, potentially mid-circuit, measurements. In this work, we first observe that the pattern of increase in the squeezing of the probes is applicable even to states with some non-Gaussian features. We then propose an experimentally feasible version of this phase estimation scheme, based on the alternating application of one-axis twist (OAT) operations and rotations. Our protocols are explicitly described in terms of multiple OAT angles whose durations decrease polynomially with system size and spin-squeezing parameters that decay as N−μN^{-μ}N−μ, with μ>2/3μ>2/3μ>2/3 in most cases. Using numerical computation of the system-size dependence N−νN^{-ν}N−ν of the Bayesian mean-squared error of an estimator, we show that these states are suitable for use in the phase estimation scheme, and highlight the protocols to achieve ν=17/9ν=17/9ν=17/9 and 53/2753/2753/27 using two and three OAT operations respectively in the last adaptation stage. We also analyze the limited non-Gaussianity of the resulting probe states and discuss the role of non-Gaussianity in this protocol more generally. Finally, we analyze how robust these protocols are with respect to imperfections such as particle number fluctuations and coherent control fluctuations.
We report the first protocol specifically designed to generate anticoherent spin- j j states at different orders. The protocol consists of cycles of a rotation pulse about an axis followed by a squeezing pulse in a perpendicular direction. To protect these states, we develop dynamical decoupling techniques using group-based sequence design and the dynamically corrected gate formalism. We analyze key sources of dephasing, disorder, and dipole-dipole interactions and assess the effectiveness of our methods in preserving coherence. Potential applications of the produced anticoherent spin states include quantum sensing and studies related to quantum entanglement.
Spin cat states are promising candidates for achieving Heisenberg-limited quantum metrology. It is suggested that spin cat states can be generated by adiabatic evolution. However, due to the limited coherence time, the adiabatic process may be too slow to be practical. To speed up the state generation, we propose to use machine optimization to generate desired spin cat states. Our proposed scheme relies only on experimentally demonstrated one-axis twisting interactions with piecewise time-modulation of rotations designed via machine optimization. The required evolution time is much shorter than the one with adiabatic evolution and it does not make large modification to the existing experimental setups. Our protocol with machine optimization is efficient and easy to be implemented in state-of-the-art experiments.