  Quantum properties of optical modes are typically assessed by observing their
photon statistics or the distribution of their quadratures. Both particle- and
wave-like behaviours deliver important information, and each may be used as a
resource in quantum-enhanced technologies. Weak-field homodyne detection
provides a scheme which combines the wave- and particle-like descriptions. Here
we show that it is possible to observe a wave-like property such as the optical
coherence across Fock basis states in the detection statistics derived from
discrete photon counting. We experimentally demonstrate these correlations
using two weak-field homodyne detectors on each mode of two classes of two-mode
entangled states. Furthermore, we theoretically describe the response of
weak-field homodyne detection on a two-mode squeezed state in the context of
generalised Bell inequalities. Our work demonstrates the potential of this
technique as a tool for hybrid continuous/discrete-variable protocols on a
phenomenon that explicitly combines both approaches.
