The large-photon-number quantum state is a fundamental but nonresolved request for practical quantum information applications. We propose an N-photon state generation scheme that is feasible and scalable, using lithium niobate on insulator circuits. Such a scheme is based on the integration of a common building block called photon-number doubling unit (PDU) for deterministic single-photon parametric downconversion and upconversion. The PDU relies on a 10⁷-optical-quality-factor resonator and mW-level on-chip power, which is within the current fabrication and experimental limits. N-photon state generation schemes, with cluster and Greenberger–Horne–Zeilinger state as examples, are shown for different quantum tasks.

Quantum stochastic phase estimation has many applications in the precise measurement of various physical parameters. Similar to the estimation of a constant phase, there is a standard quantum limit for stochastic phase estimation, which can be obtained with the Mach–Zehnder interferometer and coherent input state. Recently, it has been shown that the stochastic standard quantum limit can be surpassed with nonclassical resources such as squeezed light. However, practical methods to achieve quantum enhancement in the stochastic phase estimation remain largely unexplored. Here we propose a method utilizing the SU(1,1) interferometer and coherent input states to estimate a stochastic optical phase. As an example, we investigate the Ornstein–Uhlenback stochastic phase. We analyze the performance of this method for three key estimation problems: prediction, tracking, and smoothing. The results show significant reduction of the mean square error compared with the Mach–Zehnder interferometer under the same photon number flux inside the interferometers. In particular, we show that the method with the SU(1,1) interferometer can achieve fundamental quantum scaling, achieve stochastic Heisenberg scaling, and surpass the precision of the canonical measurement.