Measuring nonlocal coherence with weak-field homodyne detection

A feature of quantum mechanical states is delocalised coherence. We directly observe this coherence up to the three photon level. Explicitly, we carry out two-mode weak-field homodyne of both a single photon split at a beam splitter and a two-mode squeezed state. While our measurements are insufficient to quantify or witness entanglement directly, with improved collection efficiency and measurement stability we aim to show that this can be achieved with such a scheme. Thus we have shown how such a detector can directly probe coherence in both the discrete and continuous variable pictures.