  The advent of structured, high-dimensional entangled states brings new
possibilities for quantum imaging, information processing and quantum key
distribution. We experimentally generate and characterize a spatially entangled
state stored in a quantum memory system, using entropic EPR-steering
inequality, yielding genuine violation of $1.06\pm0.15$ bits and certifying
entanglement of formation of at least $0.70\pm0.15$ ebits. The supremacy of the
entropic witness is demonstrated for a wide class of experimentally available
states, giving prospects for EPR-steering applications in noisy systems or with
lossy quantum channels.
