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arXiv:1701.02928 · Physical Review A

Robust guaranteed-cost adaptive quantum phase estimation

Shibdas Roy, Dominic William Berry, Ian R. Petersen, Elanor H. Huntington

Published May 11, 2017• 1 citation

Abstract

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.

DOI: 10.1103/physreva.95.052322

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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.

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It is well-known that adaptive homodyne estimation of continuously varying optical phase provides superior accuracy in the phase estimate as compared to adaptive or non-adaptive static estimation. However, most phase estimation schemes rely on precise knowledge of the underlying parameters of the system under measurement, and performance deteriorates significantly with changes in these parameters; hence it is desired to develop robust estimation techniques immune to such uncertainties. In related works, we have already shown how adaptive homodyne estimation can be made robust to uncertainty in an underlying parameter of the phase varying as a simplistic Ornstein-Uhlenbeck stochastic noise process. Here, we demonstrate robust phase estimation for a more complicated resonant noise process using a guaranteed cost robust filter.

It is well-known that adaptive homodyne estimation of continuously varying optical phase provides superior accuracy in the phase estimate as compared to adaptive or non-adaptive static estimation. However, most phase estimation schemes rely on precise knowledge of the underlying parameters of the system under measurement, and performance deteriorates significantly with changes in these parameters; hence it is desired to develop robust estimation techniques immune to such uncertainties. In related works, we have already shown how adaptive homodyne estimation can be made robust to uncertainty in an underlying parameter of the phase varying as a simplistic Ornstein-Uhlenbeck stochastic noise process. Here, we demonstrate robust phase estimation for a more complicated resonant noise process using a guaranteed cost robust filter.

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