Nonlocal quantum metrology based on entanglement and weak measurement

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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.