Quantum Fisher information and quadrature squeezing in Janus superpositions of squeezed vacua

Abstract

Janus states, defined as coherent superpositions of two single-mode squeezed vacua, provide a simple but genuinely non-Gaussian setting for studying how interference reshapes quantum Fisher information (QFI) beyond the Gaussian squeezed-vacuum picture. Using an exact analytic treatment, we determine the QFI of Janus states and identify the benchmarks under which they can or cannot offer a metrological advantage over the single squeezed vacuum. We find that, under a fair comparison at fixed mean photon number, the single squeezed vacuum remains optimal for principal second-moment squeezing, so no genuine Janus advantage exists at that level. By contrast, within a fixed two-state span, a Janus superposition can simultaneously outperform its constituents in a laboratory quadrature variance and in number-generated phase QFI. We also introduce an operational benchmark based on fixed measured squeezing and show that, at the same observed squeezing level, Janus interference can substantially enhance the QFI for quadratic-generator sensing beyond the pure-Gaussian squeezed-vacuum reference. These results show that the metrological performance of Janus states is controlled not only by quadrature squeezing, but also by higher-order fluctuations and by the benchmark used for comparison.