Optimal phase sensitivity of an unbalanced Mach-Zehnder interferometer

In this paper we address the problem of optimizing an unbalanced Mach-Zehnder interferometer, for a given pure input state and considering a specific detection scheme. While the optimum transmission coefficient of the first beam splitter can be uniquely determined via the quantum Fisher information only [Ataman, Phys. Rev. A 105 , 012604 (2022)], the second beam-splitter transmission coefficient is detection-scheme depen-dent, too. We systematically give analytic solutions for the optimum transmission coefficient of the second beam splitter for three types of widely used detection schemes. We provide detailed examples including both Gaussian and non-Gaussian input states, showing when an unbalanced Mach-Zehnder interferometer can outperform its balanced counterpart in terms of phase sensitivity.

Automated summary

This paper addresses the problem of optimizing an unbalanced Mach-Zehnder interferometer for a given pure input state and specific detection scheme. The optimum transmission coefficient of the first beam splitter can be uniquely determined using the quantum Fisher information, while the second beam splitter's transmission coefficient is also dependent on the detection scheme. The paper systematically provides analytic solutions for the optimum transmission coefficient of the second beam splitter for three widely used detection schemes. Detailed examples are provided, including both Gaussian and non-Gaussian input states, to demonstrate the advantage of an unbalanced Mach-Zehnder interferometer over its balanced counterpart in terms of phase sensitivity.