  Einstein-Podolsky-Rosen (EPR) steering describes how different ensembles of
quantum states can be remotely prepared by measuring one particle of an
entangled pair. Here, we investigate quantum steering for single quantum
d-dimensional systems (qudits) and devise efficient conditions to certify the
steerability therein, which are applicable both to single-system steering and
EPR steering. In the single-system case our steering conditions enable the
unambiguous ruling-out of generic classical means of mimicking steering. Ruling
out false-steering scenarios has implications for securing channels against
both cloning-based individual attack and coherent attacks when implementing
quantum key distribution using qudits. We also show that these steering
conditions also have applications in quantum computation, in that they can
serve as an efficient criterion for the evaluation of quantum logic gates of
arbitrary size. Finally, we describe how the non-local EPR variant of these
conditions also function as tools for identifying faithful one-way quantum
computation, secure entanglement-based quantum communication, and genuine
multipartite EPR steering.
