Informational completeness of continuous-variable measurements

TL;DR

This paper demonstrates that homodyne tomography is informationally complete when the number of measurements matches the density matrix dimension, and explores the completeness of other measurement schemes in finite-dimensional truncations.

Contribution

It establishes conditions for informational completeness of homodyne tomography and analyzes other measurement schemes in finite-dimensional settings.

Findings

Homodyne tomography is informationally complete with sufficient measurements.

Completeness of other schemes depends on the measurement and truncation.

Provides criteria for measurement scheme completeness in finite-dimensional subspaces.

Abstract

We justify that homodyne tomography turns out to be informationally complete when the number of independent quadrature measurements is equal to the dimension of the density matrix in the Fock representation. Using this as our thread, we examine the completeness of other schemes, when continuous-variable observations are truncated to discrete finite-dimensional subspaces.