Characterizing the performance of continuous-variable Gaussian quantum gates

The required set of operations for universal continuous-variable quantum computation can be primarily be divided into two categories: Gaussian and non-Gaussian operations. Furthermore, any Gaussian operation can be decomposed as a sequence of phase-space displacements and symplectic transformations. Although Gaussian operations are ubiquitous in quantum optics, their experimental realizations are generally approximations of the ideal Gaussian unitaries. In this work, we study different performance metrics to analyze how well these experimental approximations simulate the ideal Gaussian operations. In particular, we find that none of these experimental approximations converge uniformly to the ideal Gaussian processes. However, convergence occurs in the strong sense, or if the discrimination strategy is energy bounded, then the convergence is uniform. We indicate how these energy-constrained bounds could be used for experimental implementations of these Gaussian operations in order to achieve any desired accuracy.