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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.
Einstein, Podolsky and Rosen (EPR) pointed out that the quantum-mechanical description of physical reality implied an unphysical, instantaneous action between distant measurements. To avoid such an action at a distance, EPR concluded that Quantum Mec
EPR steering is an asymmetric form of correlations which is intermediate between quantum entanglement and Bell nonlocality, and can be exploited for quantum communication with one untrusted party. In particular, steering of continuous variable Gaussi
Einstein-Podolsky-Rosen (EPR) steering is a form of bipartite quantum correlation that is intermediate between entanglement and Bell nonlocality. It allows for entanglement certification when the measurements performed by one of the parties are not c
We investigate the separability of the two-mode Gaussian states by using the variances of a pair of Einstein-Podolsky-Rosen (EPR)-like observables. Our starting point is inspired by the general necessary condition of separability introduced by Duan {
We consider the uncertainty bound on the sum of variances of two incompatible observables in order to derive a corresponding steering inequality. Our steering criterion when applied to discrete variables yields the optimum steering range for two qubi