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Large optical nonlinearities can have numerous applications, ranging from thegeneration of cat-states for optical quantum computation, through to quantumsensing where the sensitivity exceeds Heisenberg scaling in the resources.However, the generation of ultra-large optical nonlinearities has provedimmensely challenging experimentally. We describe a novel protocol where onecan effectively generate large optical nonlinearities via the conditionalapplication of a linear operation on an optical mode by an ancilla mode,followed by a measurement of the ancilla and corrective operation on the probemode. Our protocol can generate high quality optical Schr{\"{o}}dinger catstates useful for optical quantum computing and can be used to perform sensingof an unknown rotation or displacement in phase space, with super-Heisenbergscaling in the resources. We finally describe a potential experimentalimplementation using atomic ensembles interacting with optical modes via theFaraday effect.

Generating nonlinearities from conditional linear operations, squeezing and measurement for quantum computation and super-Heisenberg sensing