# Joint measurement of complementary observables in moment tomography

## TL;DR

This paper develops a general theory comparing heterodyning and homodyning in quantum state tomography, showing heterodyning's superior performance for certain quantum states and extending the analysis to two-mode sources.

## Contribution

It introduces a comprehensive framework for understanding the measurement power of heterodyning versus homodyning in quantum tomography, including two-mode systems.

## Key findings

- Heterodyning can outperform balanced homodyning in state reconstruction accuracy.
- The theory applies to various classes of single-mode quantum states.
- Extension of the analysis to two-mode quantum sources.

## Abstract

Wigner and Husimi quasi-distributions, owing to their functional regularity, give the two archetypal and equivalent representations of all observable-parameters in continuous-variable quantum information. Balanced homodyning and heterodyning that correspond to their associated sampling procedures, on the other hand, fare very differently concerning their state or parameter reconstruction accuracies. We present a general theory of a now-known fact that heterodyning can be tomographically more powerful than balanced homodyning to many interesting classes of single-mode quantum states, and discuss the treatment for two-mode sources.