连续测量量子系统中漂移参数的快速估计
Rapid estimation of drifting parameters in continuously measured quantum systems
摘要：
研究了连续测量下量子系统中哈密顿参量的确定问题。我们展示了一种计算快速但统计上最优的方法来估计一个未知的和可能的时间依赖性参数，在那里我们最大限度地提高所观察到的随机读出的可能性。通过直接处理原始测量记录而不是量子态轨迹，可以在获取数据的同时执行估计，从而允许在缓慢漂移期间实时地连续跟踪参数。此外，我们将现实的非理想性，如退相干过程和测量效率低下。作为一个例子，我们专注于连续测量量子比特的拉比频率的值的估计，并比较极大似然估计一个更简单的快速傅立叶变换。使用这个例子，我们讨论的估计的质量如何取决于测量的强度和持续时间，我们还讨论了估计的准确性和漂移的敏感性之间的权衡估计持续时间是不同的。
英文摘要：
We investigate the determination of a Hamiltonian parameter in a quantum system undergoing continuous measurement. We demonstrate a computationally rapid yet statistically optimal method to estimate an unknown and possibly time-dependent parameter, where we maximize the likelihood of the observed stochastic readout. By dealing directly with the raw measurement record rather than the quantum state trajectories, the estimation can be performed while the data is being acquired, permitting continuous tracking of the parameter during slow drifts in real time. Furthermore, we incorporate realistic nonidealities, such as decoherence processes and measurement inefficiency. As an example, we focus on estimating the value of the Rabi frequency of a continuously measured qubit, and compare maximum likelihood estimation to a simpler fast Fourier transform. Using this example, we discuss how the quality of the estimation depends on both the strength and duration of the measurement; we also discuss the trade-off between the accuracy of the estimate and the sensitivity to drift as the estimation duration is varied.
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