Abstract
In this paper, we propose a new, to the best of our knowledge, protocol that enables two distant parties to prepare a photon hyperstate for each other encoded at the same time in both polarization and spatial-mode degrees of freedom. The bidirectional remote hyperstate preparation is demanded so that it is remotely controllable by a common supervisor. Such a task appears possible using a shared quantum channel made of five photons entangled simultaneously in the two corresponding degrees of freedom, the so-called hyperentanglement. We first design a near-deterministic scheme to produce a relevant five-photon hyperentanagled state to be served as the working nonlocal channel and then present our protocol for controlled bidirectional remote hyperstate preparation, which always is successful.
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