# Tuning between photon-number and quadrature measurements with weak-field homodyne detection

## TL;DR

This paper demonstrates an experimental weak-field homodyne detector capable of continuously tuning between photon-number and quadrature measurements, enhancing quantum state analysis and engineering.

## Contribution

The authors experimentally implement a tunable weak-field homodyne detector that bridges photon-number and quadrature measurements, enabling optimized quantum property testing and state preparation.

## Key findings

- Discrete difference statistics converge to quadrature distribution with increased coherent amplitude
- Controlled photon-number distribution of heralded states demonstrated
- Detector enables continuous measurement operator tuning

## Abstract

Variable measurement operators enable the optimization of strategies for testing quantum properties and the preparation of a range of quantum states. Here, we experimentally implement a weak-field homodyne detector that can continuously tune between measuring photon numbers and field quadratures. We combine a quantum signal with a coherent state on a balanced beam splitter and detect light at both output ports using photon-number-resolving transition edge sensors. We observe that the discrete difference statistics converge to the quadrature distribution of the signal as we increase the coherent state amplitude. Moreover, in a proof-of-principle demonstration of state engineering, we show the ability to control the photon-number distribution of a state that is heralded using our weak-field homodyne detector.