Highly accurate Gaussian process tomography with geometrical sets of coherent states

TL;DR

This paper introduces a geometrical set of input coherent states for efficient and highly accurate Gaussian process tomography, reducing the need for prior process knowledge and outperforming other strategies in typical scenarios.

Contribution

The authors develop a geometrical set of input states that nearly optimally reconstruct Gaussian processes without prior process information, improving efficiency and accuracy.

Findings

Geometrical set achieves near-optimal reconstruction accuracy.

Method outperforms nonadaptive strategies for typical Gaussian processes.

Effective with low-energy coherent states.

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 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 trace-preserving Gaussian processes of typical parameter ranges so long as the displacement components are not too large.