  Einstein-Podolsky-Rosen (EPR) steering allows two parties to verify their
entanglement, even if one party's measurements are untrusted. This concept has
not only provided new insights into the nature of non-local spatial
correlations in quantum mechanics, but also serves as a resource for one-sided
device-independent quantum information tasks. Here, we investigate how EPR
steering behaves when one-half of a maximally-entangled pair of qudits
(multidimensional quantum systems) is cloned by a universal cloning machine. We
find that EPR steering, as verified by a criterion based on the mutual
information between qudits, can only be found in one of the copy subsystems but
not both. We prove that this is also true for the single-system analogue of EPR
steering. We find that this restriction, which we term "no-cloning of quantum
steering", elucidates the physical reason why steering can be used to secure
sources and channels against cloning-based attacks when implementing quantum
communication and quantum computation protocols.
