  Einstein-Podolsky-Rosen (EPR) steering is the explicit demonstration of the
fact that the measurements of one party can in influence the quantum state held
by another, distant, party, and do so even if the measurements themselves are
untrusted. This has been shown to allow one-sided device-independent
quantum-information tasks between two remote parties. However, in general,
advanced multiparty protocols for generic quantum technologies, such as quantum
secret sharing and blind quantum computing for quantum networks, demand
multipartite quantum correlations of graph states shared between more than two
parties. Here, we show that, when one part of a quantum multidimensional system
composed of a two-colorable graph state (e.g., cluster and
Greenberger-Horne-Zeilinger states) is attacked by an eavesdropper using a
universal cloning machine, only one of the copy subsystems can exhibit
multipartite EPR steering but not both. Such a no-sharing restriction secures
both state sources and channels against cloning-based attacks for generic
quantum networking tasks, such as distributed quantum-information processing,
in the presence of uncharacterized measurement apparatuses.
