Nonlocal quantum metrology based on entanglement and weak measurement

我们在光-物质界面中建立了法拉第相互作用来评估误差、干扰，并检验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，我们观察到由法拉第旋转和自旋旋转引起的误差和扰动的循环振荡。这种行为是逆作用效应对自旋系统的影响，它扰乱（旋转）了布洛赫球上的自旋。类似地，我们使用光的相空间近似来研究偏振压缩光的情况，其中压缩参数作为测量强度以及光与自旋之间的耦合发生。最后，我们给出了上述情况下的误差-扰动关系，并证明heisenberg - arthur - kelly不确定性可以被打破，而紧的Branciard-Ozawa不确定性总是成立。我们的分析有助于理解原子-光界面框架下自旋测量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部完全贝尔态测量的方案。我们在小型量子计算机（IBM-Q）上实现并演示了该协议，并考虑到所使用的门和量子位的现有误差和噪声，分析了测量的保真度。该方案可以实现可变测量强度的非局部广义贝尔状态测量。

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.