Full tomography from compatible measurements

TL;DR

This paper introduces a quantum tomography method that leverages compatible measurements and prior information to efficiently reconstruct complex quantum states, demonstrated through photonic vortex experiments.

Contribution

It presents a novel tomography scheme that reduces detection complexity by utilizing prior information and compatible measurements, enhancing efficiency in quantum state reconstruction.

Findings

Effective reconstruction of photonic vortices demonstrated

Reduction in detection complexity achieved

Prior information improves tomography accuracy

Abstract

We put forward a reconstruction scheme prompted by the relation between a von Neumann measurement and the corresponding informationally complete measurement induced in a relevant reconstruction subspace. This method is specially suited for the full tomography of complex quantum systems, where the intricacies of the detection part of the experiment can be greatly reduced provided some prior information is available. In broader terms this shows the importance of \sugg{this often-disregarded} prior information in quantum theory. The proposed technique is illustrated with an experimental tomography of photonic vortices of moderate dimension.