Standard Quantum Limit and Heisenberg Limit in Function Estimation
Standard Quantum Limit and Heisenberg Limit in Function Estimation
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DOI：
10.1103/physrevlett.124.010507
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发表时间：
2020-01-08
影响因子：
8.6
通讯作者：
Ueda, Masahito
中科院分区：
文献类型：
--
作者：
Kura, Naoto;Ueda, Masahito
与已建立的参数估计不同，函数估计尽管具有巨大的潜在效用，但仍面临概念和数学上的困难。我们建立了量子计量中考虑不同程度光滑函数的空间变化相位算子函数估计的基本误差界。在不存在粒子间纠缠和存在粒子间纠缠的情况下，分别对应于标准量子极限和海森堡极限，确定了误差边界。值得注意的是，这些误差边界可以通过位置局域状态或波数局域状态达到。事实上，我们证明了这些误差范围在理论上对于任何类型的探针状态都是最优的，这表明即使经典检测被量子测量取代，函数上的量子计量也服从Nyquist-Shannon抽样定理。
Unlike well-established parameter estimation, function estimation faces conceptual and mathematical difficulties despite its enormous potential utility. We establish the fundamental error bounds on function estimation in quantum metrology for a spatially varying phase operator, where various degrees of smooth functions are considered. The error bounds are identified in the cases of the absence and the presence of interparticle entanglement, which correspond to the standard quantum limit and the Heisenberg limit, respectively. Notably, these error bounds can be reached by either position-localized states or wavenumber-localized ones. In fact, we show that these error bounds are theoretically optimal for any type of probe states, indicating that quantum metrology on functions is also subject to the Nyquist-Shannon sampling theorem, even if classical detection is replaced by quantum measurement.