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This paper proves that the remote state preparation (RSP) scheme in realHilbert space can only be implemented when the dimension of the space is 2,4 or8. This fact is shown to be related to the parallelazablity of the $n$-1dimensional sphere $S^{n-1}$. When the dimension is 4 and 8 the generalizedscheme is explicitly presented. It is also shown that for a given state withcomponents having the same norm, RSP can be generalized to arbitrary dimensioncase.Comment: 8pages, no figures, late

physical review. a, atomic, molecular, and optical physics/physical review, a, atomic, molecular, and optical physics

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Remote-state preparation in higher dimension and the parallelizable manifoldSn−1