Quantum Fisher information maximization in an unbalanced lossy interferometer
Stefan Ataman, Karunesh Kumar Mishra · Physical Review A · 2024
In this work we address the problem of quantum Fisher information (QFI) maximization in an unbalanced lossy Mach-Zehnder interferometer. We implement the scheme from Escher et al. [Nat. Phys. 7, 406 (2011)] allowing us to obtain in closed form the lossy QFI for all involved scenarios. Then, mirroring the lossless case Ataman [Phys. Rev. A 105, 012604 (2022)], by optimizing the transmission coefficient of the first beam splitter, we maximize each QFI in question. We consider this problem for both single- and two-parameter QFI, i.e., for the scenarios with or without access to an external phase reference. Contrary to the lossless case, calculations are much more involved, however, we are able to put forward a large number of results in closed form. We also introduce two concepts, the balanced penalty and the QFI loss rate. Finally, we thoroughly discuss our results through a number of examples, including both Gaussian and non-Gaussian input states.