Highly accurate Gaussian process tomography with geometrical sets of coherent states

Abstract

Abstract We propose a practical strategy for choosing sets of input coherent states that are near-optimal for reconstructing single-mode Gaussian quantum processes with output-state heterodyne measurements. We first derive analytical expressions for the mean squared-error that quantifies the reconstruction accuracy for general process tomography and large data. Using such expressions, upon relaxing the trace-preserving (TP) constraint, we introduce an error-reducing set of input coherent states that is independent of the measurement data or the unknown true process—the geometrical set. We numerically show that process reconstruction from such input coherent states is nearly as accurate as that from the best possible set of coherent states chosen with the complete knowledge about the process. This allows us to efficiently characterize Gaussian processes even with reasonably low-energy coherent states. We numerically observe that the geometrical strategy without trace preservation beats all nonadaptive strategies for arbitrary TP Gaussian processes of typical parameter ranges so long as the displacement components are not too large.