Tighter Einstein-Podolsky-Rosen steering inequality based on the sum-uncertainty relation

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-qubit Werner states in the two-measurement and two-outcome scenario. We further employ the derived steering relation for several classes of continuous-variable systems. We show that non-Gaussian entangled states such as the photon-subtracted squeezed vacuum state and the two-dimensional harmonic-oscillator state furnish greater violation of the sum steering relation compared to the Reid criterion as well as the entropic steering criterion. The sum steering inequality provides a tighter steering condition to reveal the steerability of continuous-variable states.