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arXiv:1412.4963 · New Journal of Physics

Robust adaptive quantum phase estimation

Shibdas Roy, Ian R. Petersen, Elanor H. Huntington

Published Jun 16, 2015• 12 citations
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Abstract

Quantum parameter estimation is central to many fields such as quantum computation, communications and metrology. Optimal estimation theory has been instrumental in achieving the best accuracy in quantum parameter estimation, which is possible when we have very precise knowledge of and control over the model. However, uncertainties in key parameters underlying the system are unavoidable and may impact the quality of the estimate. We show here how quantum optical phase estimation of a squeezed state of light exhibits improvement when using a robust fixed-interval smoother designed with uncertainties explicitly introduced in parameters underlying the phase noise.

DOI
10.1088/1367-2630/17/6/063020

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Quantum parameter estimation is central to many fields such as quantum computation, communications and metrology. Optimal estimation theory has been instrumental in achieving the best accuracy in quantum parameter estimation, which is possible when we have very precise knowledge of and control over the model. However, uncertainties in key parameters underlying the system are unavoidable and may impact the quality of the estimate. We show here how quantum optical phase estimation of a squeezed state of light exhibits improvement when using a robust fixed-interval smoother designed with uncertainties explicitly introduced in parameters underlying the phase noise.
Quantum parameter estimation plays a key role in many fields like quantum computation, communication, and metrology. Optimal estimation allows one to achieve the most precise parameter estimates, but requires accurate knowledge of the model. Any inevitable uncertainty in the model parameters may heavily degrade the quality of the estimate. It is therefore desired to make the estimation process robust to such uncertainties. Robust estimation was previously studied for a varying phase, where the goal was to estimate the phase at some time in the past, using the measurement results from both before and after that time within a fixed time interval up to current time. Here, we consider a robust guaranteed-cost filter yielding robust estimates of a varying phase in real time, where the current phase is estimated using only past measurements. Our filter minimizes the largest (worst-case) variance in the allowable range of the uncertain model parameter(s) and this determines its guaranteed cost. It outperforms in the worst case the optimal Kalman filter designed for the model with no uncertainty, which corresponds to the center of the possible range of the uncertain parameter(s). Moreover, unlike the Kalman filter, our filter in the worst case always performs better than the best achievable variance for heterodyne measurements, which we consider as the tolerable threshold for our system. Furthermore, we consider effective quantum efficiency and effective noise power, and show that our filter provides the best results by these measures in the worst case.
Adaptive homodyne estimation of a continuously evolving optical phase using time-symmetric quantum smoothing has been demonstrated experimentally to provide superior accuracy in the phase estimate compared to adaptive or non-adaptive estimation using filtering alone. Here, we illustrate how the mean-square error in the adaptive phase estimate may be further reduced below the standard quantum limit for the stochastic noise process considered by using a Rauch-Tung-Striebel smoother as the estimator, along with an optimal Kalman filter in the feedback loop. Further, the estimation using smoothing can be made robust to uncertainties in the underlying parameters of the noise process modulating the system phase to be estimated. This has been done using a robust fixed-interval smoother designed for uncertain systems satisfying a certain integral quadratic constraint.
Squeezed light enables quantum-enhanced phase estimation, with crucial applications in both fundamental physics and emerging technologies. To fully exploit the advantage provided by this approach, estimation protocols must remain optimal across the entire parameter range and resilient to instabilities in the probe state. In this context, strategies that rely on pre-calibrated squeezing levels are vulnerable to degradation over time and become sub-optimal when experimental conditions fluctuate. Here, we develop an adaptive multiparameter estimation strategy for ab-initio phase estimation, achieving sub-shot noise limit precision in the full periodicity interval [0, π), without relying on prior knowledge of the squeezing parameter. Our approach employs real-time feedback to jointly estimate both the optical phase and the squeezing level, ensuring robustness against experimental drifts and calibration errors. This self-calibrating scheme establishes a reliable quantum-enhanced sensing framework, opening new routes for practical scenarios and scalable distributed sensor networks using squeezed light.
Continuous phase estimation is known to be superior in accuracy as compared to static estimation. The estimation process is, however, desired to be made robust to uncertainties in the underlying parameters. Here, homodyne phase estimation of coherent and squeezed states of light, evolving continuously under the influence of a second-order resonant noise process, are made robust to parameter uncertainties using a robust fixed-interval smoother, designed for uncertain systems satisfying a certain integral quadratic constraint. We observe that such a robust smoother provides improved worst-case performance over the optimal smoother and also performs better than a robust filter for the uncertain system.