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In comparison with entanglement and Bell nonlocality, Einstein-Podolsky-Rosensteering is a newly emerged research topic and in its incipient stage. AlthoughEinstein-Podolsky-Rosen steering has been explored via violations of steeringinequalities both theoretically and experimentally, the known inequalities inthe literatures are far from well-developed. As a result, it is not yetpossible to observe Einstein-Podolsky-Rosen steering for some steerable mixedstates. Recently, a simple approach was presented to identifyEinstein-Podolsky-Rosen steering based on all-versus-nothing argument, offeringa strong condition to witness the steerability of a family of two-qubit (pureor mixed) entangled states. In this work, we show that the all-versus-nothingproof of Einstein-Podolsky-Rosen steering can be tested by measuring theprojective probabilities. Through the bound of probabilities imposed bylocal-hidden-state model, the proposed test shows that steering can be detectedby the all-versus-nothing argument experimentally even in the presence ofimprecision and errors. Our test can be implemented in many physical systemsand we discuss the possible realizations of our scheme with non-Abelian anyonsand trapped ions.

Test of Einstein-Podolsky-Rosen Steering Based on the All-Versus-Nothing Proof