A measurement-induced optical Kerr interaction

TL;DR

This paper proposes a measurement-based method to implement a weak optical Kerr interaction using ancilla states, beam splitters, squeezers, and homodyne detection, achieving high fidelity with practical approximations.

Contribution

It introduces a novel measurement-based scheme for realizing Kerr interactions that does not rely on natural nonlinearities, using ancilla states and elementary operations.

Findings

High fidelity achieved with approximate ancilla states

Deterministic implementation with about ten gate teleportations

Effective for weak coherent and single-photon superposition states

Abstract

We present a method for implementing a weak optical Kerr interaction (single-mode Kerr Hamiltonian) in a measurement-based fashion using the common set of universal elementary interactions for continuous-variable quantum computation. Our scheme is a conceptually distinct alternative to the use of naturally occurring, weak Kerr nonlinearities or specially designed nonlinear media. Instead, we propose to exploit suitable offline prepared quartic ancilla states together with beam splitters, squeezers, and homodyne detectors. For perfect ancilla states and ideal operations, our decompositions for obtaining the measurement-based Kerr Hamiltonian lead to a realization with near-unit fidelity. Nonetheless, even by using only approximate ancilla states in the form of superposition states of up to four photons, high fidelities are still attainable. Our scheme requires four elementary operations and its deterministic implementation corresponds to about ten ancilla- based gate teleportations. We test our measurement-based Kerr interaction against an ideal Kerr Hamiltonian by applying them both to weak coherent states and single-photon superposition states.