Operational quantification of continuous-variable correlations

We quantify correlations (quantum and/or classical) between two continuous-variable modes as the maximal number of correlated bits extracted via local quadrature measurements. On Gaussian states, such bit quadrature correlations majorize entanglement, reducing to an entanglement monotone for pure states. For non-Gaussian states, such as photonic Bell states, photon-subtracted states, and mixtures of Gaussian states, the bit correlations are shown to be a monotonic function of the negativity. This quantification yields a feasible, operational way to measure non-Gaussian entanglement in current experiments by means of direct homodyne detection, without a complete state tomography.