Nonlocal quantum metrology based on entanglement and weak measurement

我们在光-物质界面上建立了一个法拉第相互作用来评估误差和扰动，并考察了它们之间的不确定关系。我们研究了各种偏振光态，包括相干态和压缩相干态。在结果中，我们观察到了由法拉第旋转和自旋旋转引起的误差和扰动的周期振荡。这一行为是对自旋系统的反向作用效应的印记，自旋系统扰乱(旋转)其布洛赫球面上的自旋。类似地，我们利用光的相空间近似研究了偏振压缩光的情况，其中压缩参数作为测量强度与光与自旋之间的耦合一起发生。最后，我们建立了上述情况下的误差-扰动关系，并指出海森堡-阿尔瑟斯-凯利不确定度是可以违反的，而紧Branciard-Ozawa不确定度总是成立的。我们的分析将有助于理解原子-光界面框架下自旋测量中的误差和扰动以及不确定原理。我们还研究了利用纠缠计进行非局域、完整的Bell态测量的协议。我们在小型量子计算机(IBM-Q)上实现和演示了该协议，并分析了测量的保真度，同时考虑到所使用的门和量子比特存在的误差和噪声。该方案实现了测量强度可变的非局域广义Bell态测量。

We formulate a Faraday interaction in the light-matter interface for evaluating the error, disturbance, and examine their uncertainty relations. We investigate various polarized light states, including coherent and squeezed coherent states. In the results, we observe the cyclic oscillations for the error and disturbance resulting from the Faraday rotation and spin rotation. This behavior is the imprint of the back-action effect on the spin system that disturbs (rotates) the spin on its Bloch sphere. Similarly, we investigate the case of polarization squeezed light using the phase-space approximation for the light, where the squeezing parameter takes place as a measurement strength together with the coupling between the light and the spin. We finally formulate the error-disturbance relations in these cases above and provide that the Heisenberg-Arthurs-Kelly uncertainty can be violated while the tight Branciard-Ozawa uncertainty always holds. Our analysis would contribute to the understanding of the error and disturbance as well as the uncertainty principle in the spin measurements under the atom-light interface framework.We also investigated the protocol of nonlocal, complete Bell state measurement using entangled meter. We implemented and demonstrated the protocol on the small-scale quantum computer (IBM-Q) and analyzed the fidelity of the measurement taking account of the existing error and noise of the gates and qubits used. The scheme makes it possible to implement the nonlocal, generalized Bell state measurement with variable measurement strength.