We propose a multiphoton heralding scheme using an optical parametric amplifier (OPA) that can generate two families of non-Gaussian states from a squeezed vacuum into: large-amplitude squeezed Schrödinger cat states and low-order parity-selective Fock superpositions. By injecting $m$ photons into the idler port and detecting $n$ photons at the output, an effective high-order photon subtraction ($k\ge 3$) can be realized in a single OPA device for properly chosen ($m, n$) pairs, with an effective order $k=m+n$. The heralded states exhibit strong Wigner negativity and high phase-space complexity. Remarkably, under photon loss, the complexity remains substantial, even after the negativity vanishes, indicating a loss-resilient quantum resource. These states exhibit phase-estimation performance that can achieve Heisenberg limit scaling with an enhanced constant factor in certain regimes. Our protocol establishes the OPA as a versatile platform for generating non-Gaussian states with promising applications in loss-resilient quantum metrology and fault-tolerant quantum information processing.

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• Non-gaussian quantum states
• Quantum error correction
• Quantum information processing
• Quantum optics
• Quantum state engineering