Quantum Fisher information maximization in an unbalanced interferometer

In this paper we provide the answer to following question: given an arbitrary pure input state and a general, unbalanced, Mach-Zehnder interferometer, what transmission coefficient of first beam splitter maximizes quantum Fisher information (QFI)? We consider question for both single- two-parameter QFI, or, in other words, with or without having access external phase reference. give analytical results all involved scenarios. It turns out that, large class states, balanced (50:50) scenario yields optimal QFI; however, is far from being universal truth. When it comes single-parameter rarely one unbalanced interferometer can bring significant advantage over case. also condition imposed upon so that no metrological be exploited via Finally, illustrate discuss our assertions through number examples, including Gaussian non-Gaussian states.