  Quantum steering enables one party to communicate with another remote party
even if the sender is untrusted. Such characteristics of quantum systems not
only provide direct applications to quantum information science, but are also
conceptually important for distinguishing between quantum and classical
resources. While concrete illustrations of steering have been shown in several
experiments, quantum steering has not been certified for higher dimensional
systems. Here, we introduce a simple method to experimentally certify two
different kinds of quantum steering: Einstein-Podolsky-Rosen (EPR) steering and
single-system (SS) steering (i.e., temporal steering), for dimensionality (d)
up to d=16. The former reveals the steerability among bipartite systems,
whereas the latter manifests itself in single quantum objects. We use
multidimensional steering witnesses to verify EPR steering of
polarization-entangled pairs and SS steering of single photons. The ratios
between the measured witnesses and the maximum values achieved by classical
mimicries are observed to increase with $d$ for both EPR and SS steering. The
designed scenario offers a new method to study further the genuine multipartite
steering of large dimensionality and potential uses in quantum information
processing.
