  Quantum paradoxes are essential means to reveal the incompatibility between
quantum and classical theories, among which the Einstein-Podolsky-Rosen (EPR)
steering paradox offers a sharper criterion for the contradiction between
local-hidden-state model and quantum mechanics than the usual inequality-based
method. In this work, we present a generalized EPR steering paradox, which
predicts a contradictory equality $2_{Q}=\left( 1+\delta\right)_{C}$
($0\leq\delta<1$) given by the quantum ($Q$) and classical ($C$) theories. For
any $N$-qubit state in which the conditional state of the steered party is
pure, we test the paradox through a two-setting steering protocol, and find
that the state is steerable if some specific measurement requirements are
satisfied. Moreover, our construction also enlightens the building of EPR
steering inequality, which may contribute to some schemes for typical quantum
teleportation and quantum key distributions.
