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Cat states and Gottesman-Kitaev-Preskill (GKP) states play a key role inquantum computation and communication with continuous variables. The creationof such states relies on strong nonlinear light-matter interactions, which arewidely available in microwave frequencies as in circuit quantum electrodynamicsplatforms. However, strong nonlinearities are hard to come by in opticalfrequencies, severely limiting the use of continuous variable quantuminformation in the optical range. Here we propose using the strong interactionsof free electrons with light as a source for optical cat and GKP states. Thestrong interactions can be realized by phase-matching of free electrons withphotonic structures such as optical waveguides and photonic crystals. Ourapproach enables the generation of optical GKP states with above 10 dBsqueezing and fidelities above 90% at post-selection probability of 10%, evenreaching >30% using an initially squeezed vacuum state. Furthermore, thefree-electron interaction allows for conditional rotations on the photonicstate, enabling to entangle a pair of GKP states into a GKP Bell state. Sinceelectrons can interact resonantly with light across the electromagneticspectrum, our approach may be used for the generation of cat and GKP statesover the entire electromagnetic spectrum, from radio-waves to X-rays.

Creation of Optical Cat and GKP States Using Shaped Free Electrons