# Towards optimal quantum tomography with unbalanced homodyning

## TL;DR

This paper demonstrates that localized unbalanced homodyning provides more accurate quantum state tomography than heterodyning or balanced homodyning, even with realistic detectors, advancing towards optimal continuous-variable quantum measurement.

## Contribution

It establishes that unbalanced homodyning is universally more powerful for quantum tomography than heterodyning across all states and schemes, including realistic detector conditions.

## Key findings

- Unbalanced homodyning outperforms heterodyning in all tested scenarios.
- Localized sampling yields more accurate estimators than delocalized methods.
- The advantage persists with subunit efficiency photodetectors.

## Abstract

Balanced homodyning, heterodyning and unbalanced homodyning are the three well-known sampling techniques used in quantum optics to characterize all possible photonic sources in continuous-variable quantum information theory. We show that for all quantum states and all observable-parameter tomography schemes, which includes the reconstructions of arbitrary operator moments and phase-space quasi-distributions, localized sampling with unbalanced homodyning is always tomographically more powerful (gives more accurate estimators) than delocalized sampling with heterodyning. The latter is recently known to often give more accurate parameter reconstructions than conventional marginalized sampling with balanced homodyning. This result also holds for realistic photodetectors with subunit efficiency. With examples from first- through fourth-moment tomography, we demonstrate that unbalanced homodyning can outperform balanced homodyning when heterodyning fails to do so. This new benchmark takes us one step towards optimal continuous-variable tomography with conventional photodetectors and minimal experimental components.