Experimentally exploring compressed sensing quantum tomography

TL;DR

This paper demonstrates that compressed sensing is an effective and resource-efficient method for quantum state tomography in photonic systems, especially when high-quality experimental data is available, enabling reliable state reconstruction.

Contribution

It provides a comprehensive analysis and a complete prescription for applying compressed sensing to quantum tomography with experimental data, including model selection and validation techniques.

Findings

Compressed sensing enables accurate quantum state reconstruction with fewer measurements.

High statistical significance of data improves the quality of tomography.

The method effectively accounts for experimental imperfections and finite data.

Abstract

In the light of the progress in quantum technologies, the task of verifying the correct functioning of processes and obtaining accurate tomographic information about quantum states becomes increasingly important. Compressed sensing, a machinery derived from the theory of signal processing, has emerged as a feasible tool to perform robust and significantly more resource-economical quantum state tomography for intermediate-sized quantum systems. In this work, we provide a comprehensive analysis of compressed sensing tomography in the regime in which tomographically complete data is available with reliable statistics from experimental observations of a multi-mode photonic architecture. Due to the fact that the data is known with high statistical significance, we are in a position to systematically explore the quality of reconstruction depending on the number of employed measurement settings, randomly selected from the complete set of data, and on different model assumptions. We present and test a complete prescription to perform efficient compressed sensing and are able to reliably use notions of model selection and cross-validation to account for experimental imperfections and finite counting statistics. Thus, we establish compressed sensing as an effective tool for quantum state tomography, specifically suited for photonic systems.