Remote state preparation in higher dimension and the parallelizable manifold $S^{n-1}$

Details Remote state preparation in higher dimension and the parallelizable manifold $S^{n-1}$ Remote state preparation in higher dimension and the parallelizable manifold $S^{n-1}$

2001-05-18

arxiv.org/abs/quant-ph/0105088v1

Physics

Quantum Physics

8pages, no figures, latex

Scientific paper

10.1103/PhysRevA.65.022316

This paper proves that the remote state preparation (RSP) scheme in real Hilbert space can only be implemented when the dimension of the space is 2,4 or 8. This fact is shown to be related to the parallelazablity of the $n$-1 dimensional sphere $S^{n-1}$. When the dimension is 4 and 8 the generalized scheme is explicitly presented. It is also shown that for a given state with components having the same norm, RSP can be generalized to arbitrary dimension case.

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