基于多光子纠缠的量子相位估计实验研究

测量是科学研究的基础，提高测量精度至关重要。在经典测量中，测量精度的极限是散粒噪声极限（Shot Noise Limit，SNL），也被称为标准量子极限（Standard Quantum Limit，SQL）；而在量子精密测量中，我们可以利用量子相干性和量子纠缠的特性提高测量灵敏度，获得超越散粒噪声极限的测量精度。利用量子资源，测量可以达到的精度极限被称为海森堡极限（Heisenberg Limit，HL）。量子精密测量技术已经应用在引力波探测、磁场探测、时间同步等多个领域。

高精度的相位估计是量子精密测量最重要的任务之一，一方面是因为很多物理量都可以投影到相位上进行测量，对于相位的高精度估计，可以用于对其他物理量的高精度测量；另一方面，量子网络已经成为量子信息领域重要的研究热点，分布式量子精密测量是量子网络的主要功能之一，实现空间位置不同的多个相位参数的高精度估计具有十分重要的应用价值。 

本人在硕士期间的主要工作是在四光子纠缠网络实验平台上完成的量子相位估计实验。我们首先将处于GHZ纠缠态的四个光子分发到四个测量节点，并在每个光子上施加一个完全未知的相位，然后根据四光子符合测量的结果，采用自适应贝叶斯推断方法实时估计四个未知相位的均值。在我们的实验中，相位估计的精度接近海森堡极限，即使在干涉可见度低至0.6时，估计精度仍然可以超越散粒噪声极限。 

本人工作的主要创新在于：首次采用贝叶斯推断算法对空间分布的相位估计进行实时估计，且相位估计的精度接近海森堡理论极限；采用基于费舍尔信息（Fisher Information）理论的自适应反馈策略，使得相位估计在整个有效参数取值空间都能达到超越散粒噪声极限的估计精度。

Measurement is an important foundation of scientific research. In classical cases, the measurement precision is limited by the shot­noise limit (SNL) ; while in quantum cases, we can exploit quantum resources, such as coherence and entanglement, to improve the measurement precision beyond the SNL and achieve the Heisenberg limit (HL). Quantum metrology has been applied in many fields such as gravitational wave detection, magnetic field detection, and time synchronization. 

Phase estimation is a key task in quantum metrology, and many physical quantities can be estimated by the phase estimation. Distributed quantum metrology (DQM), as one of the most important task in developing quantum networks has attracted a lot of attentions and has wide applications in quantum science.

In this thesis, we complete a distributed quantum phase estimation in a four­-photon entanglement quantum network. In experiments, we first distribute four photons of a GHZ state to four measurement nodes, and rotate each photon with an independent and unknown phase in its polarization space. Then we use real-time adaptive Bayesian inference to estimate the mean value of the four unknown phases based on the measurement results of the four­-photon coincidence. In our experiments, the optimal precision of the phase estimation is close to the Heisenberg limit. And in noisy case, we also experimentally verify that the estimation precision can still exceed the shot noise limit even when the visibility of four-photon GHZ is as low as 0.6.

There are two main innovations in this thesis. First, it is the first time that the real-time Bayesian inference algorithm is applied in the distributed quantum metrology to achieve an optimal precision close to the Heisenberg limit. Second, we design an adaptive strategy based on Fisher information theory, which enables the precision of the phase estimation to go beyond the SNL for the entire parameter space.

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