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The advent of structured, high-dimensional entangled states brings newpossibilities for quantum imaging, information processing and quantum keydistribution. We experimentally generate and characterize a spatially entangledstate stored in a quantum memory system, using entropic EPR-steeringinequality, yielding genuine violation of $1.06\pm0.15$ bits and certifyingentanglement of formation of at least $0.70\pm0.15$ ebits. The supremacy of theentropic witness is demonstrated for a wide class of experimentally availablestates, giving prospects for EPR-steering applications in noisy systems or withlossy quantum channels.

Certification of high-dimensional entanglement and Einstein-Podolsky-Rosen steering with cold atomic quantum memory