Squeezed optical Schrödinger cat states constitute a key resource for both fundamental tests of quantum theory and up-to-date quantum technologies. We propose a measurement-assisted gate for the generation and manipulation of the cat states. In this scheme, an ancilla in the non-Gaussian small-amplitude (in general, squeezed) Schrödinger cat state and the target oscillator initially prepared in a squeezed vacuum (or coherent) state are subjected to a quantum nondemolition (QND) entangling operation followed by projective homodyne measurement. The proposed gate enables generation of high-fidelity squeezed Schrödinger cat states with controllable size and squeezing with tunable fidelity/success-probability trade-off. We also introduce an iterative, homodyne-conditioned
CZ-based protocol for cat-state amplification. The parameter regimes required to achieve the desired fidelity and the success probability are analyzed. The approach is well suited for applications in measurement-based quantum computing and hybrid quantum networks where non-Gaussian resources enhance computational and communication capabilities.
Application of the quantum nondemolition (QND) method to Schrodinger cat states is described. Phase cat states of trapped light is generated by QND measurement of the photon number parity of a coherent field initially injected into the cavity. The measured Wigner function of a cat state at four different delays between preparation and measurement is presented. The Wigner function exhibits two positive, ideally Gaussian, peaks corresponding to the two classical components of the state. Quantitative analysis of the decoherence process is also presented. Generalization of this experiment to the preparation of non-local cat states located at the same time between two different cavities is discussed.