Optical Schrödinger cat states are non-Gaussian states with applications in quantum technologies, such as for building error-correcting states in quantum computing. Nevertheless, the efficient generation of high-fidelity optical Schrödinger cat states is an outstanding problem in quantum optics. Here we propose using squeezed superpositions of zero and two photons, $|\theta ⟩=\cos (\theta /2)|0⟩+\sin (\theta /2)|2⟩$, as ingredients for protocols to efficiently generate high-fidelity cat states. We present a protocol using linear optics with success probability $P\gtrsim 50\mathrm{\%}$ that can generate cat states of size $|\alpha {|}^2=5$ with fidelity $F>0.99$. The protocol relies only on detecting single photons and is remarkably tolerant of loss, with 2% detection loss still achieving $F>0.98$ for cat states with $|\alpha {|}^2=5$. We also show that squeezed $\theta$ states are ideal candidates for nonlinear photon subtraction using a two-level system with near-deterministic success probability and fidelity $F>0.98$ for cat states of size $|\alpha {|}^2=5$. Schemes for generating $\theta$ states using quantum emitters are also presented. Our protocols can be implemented with current state-of-the-art quantum optics experiments.

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• Non-gaussian quantum states
• Optical quantum information processing
• Photonics
• Quantum computation
• Quantum optics
• Quantum protocols
• Quantum state engineering
• Quantum states of light