Phase Diffusion Mitigation in the Truncated Mach-Zehnder Interferometer

The presence of phase diffusion noise may lead to the loss of quantum measurement advantages, resulting in measurement results that cannot beat the standard quantum limit (SQL). Squeezing is considered an effective method for reducing the detrimental effect of phase diffusion on a measurement. Reasonable use of squeezing can make a measurement exceed the SQL. The Mach-Zehnder (MZ) interferometer has been exploited as a generic tool for precise phase measurement. Describing the reduction in quantum advantage caused by phase diffusion in an MZ interferometer that can be mitigated by squeezing is not easy to handle analytically because the input state changes from a pure state to a mixed state after experiencing the diffusion noise in the MZ interferometer. We introduce a truncated MZ interferometer, a symmetrical structure that can achieve the same potential phase sensitivity as the conventional MZ interferometer. This scheme can theoretically explain how phase diffusion reduces phase estimation and why squeezing counteracts the presence of phase diffusion. Using the Gaussian property of the input state and the characteristic of Gaussian operation in the squeezing, the two orthogonal field quantities of the quantum state are squeezed and anti-squeezed to different degrees, and the analytic results are obtained. This result can beat the SQL and provide reliable theoretical guidance for the experiment. The truncated MZ interferometer is more straightforward to build and operate than the conventional MZ interferometer. Moreover, it mitigates the phase diffusion noise via the squeezing operation, thus making it useful for applications in quantum metrology.