Unitary Gate Synthesis for Continuous Variable Systems

Abstract

We investigate the synthesis of continuous-variable two-mode unitary gates in the setting where two modes A and B are coupled by a fixed quadratic Hamiltonian H. The gate synthesis consists of a sequence of evolutions governed by Hamiltonian H interspaced by local phase shifts applied to A and B. We concentrate on protocols that require the minimum necessary number of steps and we show how to implement the beam splitter and the two-mode squeezer in just three steps. Particular attention is paid to the Hamiltonian x_A p_B that describes the effective off-resonant interaction of light with the collective atomic spin.

7 pages, minor text modifications, references added

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• Conditional preparation of arbitrary atomic Dicke states
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• Quantum/Relativistic Computation of Security and Efficiency of Electrical Power System for a Day-Ahead