  In quantum information, the Werner state is a benchmark to test the boundary
between quantum mechanics and classical models. There have been three
well-known critical values for the two-qubit Werner state, i.e., $V_{\rm
c}^{\rm E}=1/3$ characterizing the boundary between entanglement and separable
model, $V_{\rm c}^{\rm B}=1/K_G(3)$ characterizing the boundary between Bell's
nonlocality and the local-hidden-variable model, while $V_{\rm c}^{\rm S}=1/2$
characterizing the boundary between Einstein-Podolsky-Rosen (EPR) steering and
the local-hidden-state model. So far, the problem of $V_{\rm c}^{\rm E}=1/3$
has been completely solved by an inequality involving in the
positive-partial-transpose criterion, while how to reveal the other two
critical values by the inequality approach are still open. In this work, we
focus on EPR steering, which is a form of quantum nonlocality intermediate
between entanglement and Bell's nonlocality. By proposing the optimal
$N$-setting linear EPR-steering inequalities, we have successfully obtained the
desired value $V_{\rm c}^{\rm S}=1/2$ for the two-qubit Werner state, thus
resolving the long-standing problem.
