Comparing Homodyne and Heterodyne Tomography of Quantum States of Light

TL;DR

This paper compares homodyne and heterodyne measurement techniques for quantum state tomography, finding homodyne generally more efficient for non-Gaussian states, with implications for optimizing quantum measurement strategies.

Contribution

It provides a theoretical and numerical comparison of homodyne and heterodyne tomography, revealing homodyne's superior efficiency for non-Gaussian states in practical scenarios.

Findings

Homodyne tomography outperforms heterodyne for all tested non-Gaussian states.

The efficiency gap between the two methods is narrower than the asymptotic bound suggests.

Results aid in optimizing measurement strategies in quantum optics.

Abstract

Non-Gaussian quantum states are critical resources in photonic quantum information processing, rendering their generation and characterization of increasing importance in quantum optics. In this work, we theoretically and numerically analyze the relative efficiency of homodyne versus heterodyne measurements for reconstructing non-Gaussian states, a major outstanding question in continuous-variable tomography. Combining a Fisher information-based formalism with simulated experiments, we find homodyne tomography to outperform heterodyne measurements for all non-Gaussian states tested, although the separation between the two modalities proves significantly narrower than suggested by the asymptotic Cramer-Rao lower bound. Our results should find use for optimizing measurement strategies in practical continuous-variable quantum systems.