  We propose a method to verify quantum steering for two qubit states with an
arbitrary amount of null results when both the steering and steered parties
cannot be trusted. We converted the steering inequality proposed in a recent
article [Phys.~Rev.~X {\bf 2}, 031003 (2012)] to a corresponding
measurement-device-independent steering criterion that depends on the heralding
efficiency of the steering party, number of measurement settings, and
imperfection of the state preparation. As a result, for a relative frequency of
valid measurement outcomes $\eta_H$, the steering can be verified using a
number of different measurement settings larger than $1/\eta_H$ and maximally
entangled states. Furthermore, steerability is guaranteed as long as the
measurement efficiency of the steered party is non-zero. Our result is useful
for loss-tolerant and measurement-device-independent steering tasks.

Quantum Physics