Performance analysis of cat and GKP breeding protocols with squeezed single-photon input

Abstract:Homodyne breeding is a promising optical route for generating large cat states and Gottesman--Kitaev--Preskill (GKP) grid states, using readily available squeezed-cat states as inputs. We analyze the performance of protocols, using squeezed single-photon seeds, $\hat{S}(r)\ket{1}$, as squeezed-cat resources and propagating them through the same cat-to-GKP breeding pipeline. For a symmetric tree with $N=2^{m_1}$ seeds, the heralded resource state reduces to a state with a polynomial-Gaussian wavefunction controlled by a single effective width, achieving near-unit fidelity with the desired cat resource state. Our analysis yields closed-form even-cat fidelities and an inverse-design rule for the seed squeezing. We apply these resources to GKP breeding, and find a large overlap with a practical GKP state. We also investigate the effects of practical imperfections, including finite homodyne acceptance windows and photon loss. This study shows that squeezed single-photon inputs provide a viable resource assignment for homodyne cat and GKP breeding, replacing the demanding requirement for high-resolution photon-number-resolving heralding with an on-demand single-photon source.

arXiv:2611.02547 [quant-ph]

(or arXiv:2611.02547v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2611.02547 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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