  Certification and quantification of correlations for multipartite states of
quantum systems appear to be a central task in quantum information theory. We
give here a unitary quantum-mechanical perspective of both entanglement and
Einstein-Podolsky-Rosen (EPR) steering of continuous-variable multimode states.
This originates in the Heisenberg uncertainty relations for the canonical
quadrature operators of the modes. Correlations of two-party $(N\, \text{vs}
\,1)$-mode states are examined by using the variances of a pair of suitable
EPR-like observables. It turns out that the uncertainty sum of these nonlocal
variables is bounded from below by local uncertainties and is strengthened
differently for separable states and for each one-way unsteerable ones. The
analysis of the minimal properly normalized sums of these variances yields
necessary conditions of separability and EPR unsteerability of $(N\, \text{vs}
\,1)$-mode states in both possible ways of steering. When the states and the
performed measurements are Gaussian, then these conditions are precisely the
previously-known criteria of separability and one-way unsteerability.
