Towards higher precision and operational use of optical homodyne tomograms

TL;DR

This paper demonstrates an operational method for analyzing optical homodyne tomograms to determine quantum state purity and uncertainty relations without state reconstruction, improving precision through error analysis and postselection.

Contribution

It introduces a direct analysis technique for optical tomograms to assess state purity and uncertainty relations, bypassing traditional reconstruction methods.

Findings

Validated the method with coherent and photon-added states

Achieved higher precision by error analysis and postselection

First experimental verification of purity-dependent uncertainty relations

Abstract

We present the results of an operational use of experimentally measured optical tomograms to determine state characteristics (purity) avoiding any reconstruction of quasiprobabilities. We also develop a natural way how to estimate the errors (including both statistical and systematic ones) by an analysis of the experimental data themselves. Precision of the experiment can be increased by postselecting the data with minimal (systematic) errors. We demonstrate those techniques by considering coherent and photon-added coherent states measured via the time-domain improved homodyne detection. The operational use and precision of the data allowed us to check for the first time purity-dependent uncertainty relations and uncertainty relations for Shannon and R\'{e}nyi entropies.