# Tuning between photon-number and quadrature measurements with weak-field homodyne detection. (arXiv:1908.04765v1 [quant-ph])

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 performing a photon-number measurement and a field
quadrature measurement on a quantum state $\hat{\rho}$. We combine $\hat{\rho}$
with a coherent state $|\alpha\rangle$ 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 $\hat{\rho}$ as we increase $|\alpha|$. 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.