Continuous variable tomographic measurements

TL;DR

This paper develops a mathematical framework to relate different quantum measurement techniques in continuous variable systems, enhancing understanding of quantum homodyne tomography and its experimental implementations.

Contribution

It constructs a generalized Markov kernel linking homodyne tomography to phase space observables and discusses the quantum justification of experimental methods.

Findings

Established a Markov kernel connecting measurement statistics

Analyzed the inverse transformation between observables

Provided remarks on experimental implementation justifications

Abstract

Using a recent result of Albini et al. to represent quantum homodyne tomography in terms of a single observable (as a normalized positive operator measure) we construct a generalized Markov kernel which transforms (the measurement outcome statistics of) this observable into (the measurement outcome statistics of) a covariant phase space observable. We also consider the inverse question. Finally, we add some remarks on the quantum theoretical justification of the experimental implementations of these observables in terms of balanced homodyne and 8-port detection techniques, respectively.