Improving the sensitivity of Kerr quantum nondemolition measurement via squeezed light

In S. N. Balybin et al. [Phys. Rev. A 106, 013720 (2022)] the scheme of quantum nondemolition measurement of optical quanta that uses a resonantly enhanced Kerr nonlinearity in optical microresonators was analyzed theoretically. It was shown that using modern high-$Q$ microresonators, it is possible to achieve sensitivity several times better than the standard quantum limit. Here we propose and analyze in detail a significantly improved version of that scheme. We show that by using a squeezed quantum state of the probe beam and the antisqueezing (parametric amplification) of this beam at the output of the microresonator, it is possible to reduce the measurement imprecision by about one order of magnitude. The resulting sensitivity allows us to generate and verify multiphoton non-Gaussian quantum states of light, making the scheme considered here interesting for quantum information processing tasks.