  We study collective `free-space' radiation properties of two distant
single-layer arrays of quantum emitters as two-level atoms. We show that this
system can support a long-lived Bell superposition state of atomic excitations
exhibiting strong subradiance, which corresponds to a non-local excitation of
the two arrays. We describe the preparation of these states and their
application in quantum information as resource of non-local entanglement,
including deterministic quantum state transfer with high fidelity between the
arrays representing quantum memories. We discuss experimental realizations
using cold atoms in optical trap arrays with subwavelength spacing, and analyze
the role of imperfections.
