  The strange property of the Einstein-Podolsky-Rosen (EPR) correlation between
two remote physical systems is a primitive object on the study of quantum
entanglement. In order to understand the entanglement in canonical
continuous-variable systems, a pair of the EPR-like uncertainties is an
essential tool. Here, we consider a normalized pair of the EPR-like
uncertainties and introduce a state-overlap to a classically correlated mixture
of coherent states. The separable condition associated with this state-overlap
determines the strength of the EPR-like correlation on a coherent-state basis
in order that the state is entangled. We show that the coherent-state-based
condition is capable of detecting the class of two-mode Gaussian entangled
states. We also present an experimental measurement scheme for estimation of
the state-overlap by a heterodyne measurement and a photon detection with a
feedforward operation.
