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Physical Review A

Measurement-induced continuous-variable quantum interactions

Radim Filip, Petr Marek, Ulrik L. Andersen

Published Apr 4, 2005• 151 citations
Publisher

Abstract

We propose feasible implementations of basic continuous-variable (CV) interactions (squeezer, parametric amplifier, and quantum nondemolition interaction) between light modes without the requirement for in-line nonlinear couplings in a strongly pumped optical medium. The method is based entirely on linear optics, homodyne detection, and off-line squeezed ancillary states and therefore represents the CV analog of the measurement-induced nonlinearity approach, previously used in single-photon qubit experiments to probabilistically implement a controlled-NOT gate.

DOI
10.1103/physreva.71.042308

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We propose general methodology of deterministic single-mode quantum interaction nonlinearly modifying single quadrature variable of a continuous-variable system. The methodology is based on linear coupling of the system to ancillary systems subsequently measured by quadrature detectors. The nonlinear interaction is obtained by using the data from the quadrature detection for dynamical manipulation of the coupling parameters. This measurement-induced methodology enables direct realization of arbitrary nonlinear quadrature interactions without the need to construct them from the lowest-order gates. Such nonlinear interactions are crucial for more practical and efficient manipulation of continuous quadrature variables as well as qubits encoded in continuous-variable systems.
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 off-line 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 10 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.
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The quantum nondemolition (QND) measurement is one of the most studied quantum measurement procedures. Usually, such a process involves the coupling of a single system of interest, called signal, with a single probe system, so that the relevant information in the signal system is indirectly measured by observing the probe system. Here we extend the concept of quantum nondemolition interaction to the cases in which the signal and the probe systems are each one multipartite continuous-variable system. Specifically, we propose a general scheme that performs the multipartite QND interactions, relying on beam-splitter couplings between the signal and probe modes with only two ancillary modes prepared offline in squeezed states. The scheme is also composed of homodyne detection and feedforward modulation. The ancillary modes are detected in the process, providing photocurrents for postmodulation of the output systems, as well as sufficient information to calculate genuine multipartite entanglement conditions of the input systems and to monitor similar conditions of the output systems.