  In comparison with entanglement and Bell nonlocality, Einstein-Podolsky-Rosen
steering is a newly emerged research topic and in its incipient stage. Although
Einstein-Podolsky-Rosen steering has been explored via violations of steering
inequalities both theoretically and experimentally, the known inequalities in
the literatures are far from well-developed. As a result, it is not yet
possible to observe Einstein-Podolsky-Rosen steering for some steerable mixed
states. Recently, a simple approach was presented to identify
Einstein-Podolsky-Rosen steering based on all-versus-nothing argument, offering
a strong condition to witness the steerability of a family of two-qubit (pure
or mixed) entangled states. In this work, we show that the all-versus-nothing
proof of Einstein-Podolsky-Rosen steering can be tested by measuring the
projective probabilities. Through the bound of probabilities imposed by
local-hidden-state model, the proposed test shows that steering can be detected
by the all-versus-nothing argument experimentally even in the presence of
imprecision and errors. Our test can be implemented in many physical systems
and we discuss the possible realizations of our scheme with non-Abelian anyons
and trapped ions.
