Phase estimation with squeezed single photons

We address the performance of an interferometric setup in which a squeezed single photon interferes at a beam splitter with a coherent state. Our analysis in based on both the quantum Fisher information and the sensitivity when a Mach-Zehnder setup is considered and the difference photocurrent is detected at the output. We compare our results with those obtained feeding the interferometer with a squeezed vacuum (with the same squeezing parameter of the squeezed single photon) and a coherent state in order to have the same total number of photons circulating in the interferometer. We find that for fixed squeezing parameter and total number of photons there is a threshold of the coherent amplitude interfering with the squeezed single photon above which the squeezed single photons outperform the performance of squeezed vacuum (showing the highest quantum Fisher information). When the difference photocurrent measurement is considered, we can always find a threshold of the squeezing parameter (given the total number of photons and the coherent amplitude) above which squeezed single photons can be exploited to reach a better sensitivity with respect to the use of squeezed vacuum states also in the presence of non unit quantum efficiency.