Quantum parameter estimation exploits quantum states to achieve estimation sensitivity beyond classical limit. In continuous variable (CV) regime, squeezed state has been exploited to implement deterministic phase estimation. It is however, often restricted by fragility of quantum states. The quantum phase estimation sensitivity of squeezed state is significantly affected by loss or detection inefficiency, which restrict its applications. This issue can be solved by using a method of parametric amplification of squeezed state \cite{OPA}. In this work, we implement multi-phase estimation with optical parametric amplification of entanglement generated from squeezed states. We find multi-phase estimation sensitivity is robust against loss or detection inefficiency, where we use two-mode Einstein-Podolsky-Rosen entangled state and four-mode cluster state for analysis. Our work provides a method for realizing large-scale quantum metrology in real-world applications against loss or detection inefficiency.
The scheme of an active interferometer for amplification of small optical signals for their subsequent photodetection is proposed. The scheme provides a considerable amplification of signals by preserving their quantum-statistical properties (ideal amplification) and also can improve these properties under certain conditions. The two-mode squeezed state of light produced upon four-wave mixing, which is used for signal amplification, can be transformed to the non-classical state of the output field squeezed in the number of photons. The scheme is phase-sensitive upon amplification of the input coherent signal. It is shown that in the case of the incoherent input signal with the average number of photons ⟨ n s ⟩∼1, the amplification process introduces no additional quantum noise at signal amplification as large as is wished. A scheme is also proposed for the cascade small-signal amplification (⟨ n s ⟩∼1) in the coherent state producing the amplified signal in the squeezed sub-Poisson state, which can be used for the high-resolution detection of weak and ultraweak optical signals.
We introduce a programmable optical parametric amplifier (OPA) synthesizer that, under a heralded photon-number-resolving framework, generates high-fidelity cubic phase states and amplifies Schrodinger cat states. By systematically exploring both the catalytic configuration, where the idler input and output contain the same number of photons (
m=n), and non-catalytic configurations (
m=n), we discover two qualitatively different functionalities. First, with a coherent-state signal input, our protocol generates cubic phase states with fidelity exceeding 0.99 across a broad range of
(m,n) configurations. Second, using a Schrödinger cat state as the signal input, the same framework amplifies the cat state: an input cat with amplitude
αin≤1 is transformed into an output squeezed cat with
αout≥2 while maintaining fidelity above 0.99. The catalytic configuration preserves the input parity and restores the idler state, whereas non-catalytic configurations enable parity-flipping amplification with higher success rates. Moreover, the amplified output can serve as a seed for subsequent amplification rounds, offering a self-seeding pathway to progressively larger cat states. Our protocol requires only moderate-gain OPA operation and low-order photon-number-resolving detection, providing a flexible and experimentally accessible platform for cubic phase state preparation and amplified squeezed cat state generation.