  Einstein-Podolsky-Rosen (EPR) steering is the ability that an observer
persuades a distant observer to share entanglement by making local
measurements. Determining a quantum state is steerable or unsteerable remains
an open problem. Here, we derive a new steering inequality with infinite
measurements corresponding to an arbitrary two-qubit T state, from
consideration of EPR steering inequalities with N projective measurement
settings for each side. In fact, the steering inequality is also a sufficient
criterion for guaranteering that the T state is unsteerable. Hence, the
steering inequality can be viewed as a necessary and sufficient criterion to
distinguish whether the T state is steerable or unsteerable. In order to reveal
the fact that the set composed of steerable states is the strict subset of the
set made up of entangled states, we prove theoretically that all separable T
states can not violate the steering inequality. Moreover, we put forward a
method to estimate the maximum violation from concurrence for arbitrary
two-qubit T states, which indicates that the T state is steerable if its
concurrence exceeds 1/4.
