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Einstein-Podolsky-Rosen (EPR) steering is the ability that an observerpersuades a distant observer to share entanglement by making localmeasurements. Determining a quantum state is steerable or unsteerable remainsan open problem. Here, we derive a new steering inequality with infinitemeasurements corresponding to an arbitrary two-qubit T state, fromconsideration of EPR steering inequalities with N projective measurementsettings for each side. In fact, the steering inequality is also a sufficientcriterion for guaranteering that the T state is unsteerable. Hence, thesteering inequality can be viewed as a necessary and sufficient criterion todistinguish whether the T state is steerable or unsteerable. In order to revealthe fact that the set composed of steerable states is the strict subset of theset made up of entangled states, we prove theoretically that all separable Tstates can not violate the steering inequality. Moreover, we put forward amethod to estimate the maximum violation from concurrence for arbitrarytwo-qubit T states, which indicates that the T state is steerable if itsconcurrence exceeds 1/4.

Necessary and sufficient criterion of steering for two-qubit T states