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This paper has been withdrawn by the author(s), due a crucial error on the entanglement of $\Gamma$ registers.

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This paper has been withdrawn by the author due to a crucial error in the submission action.

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This paper has been withdrawn by the author due to similarity to the author's other paper

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This paper has been withdrawn by the authors, as it was combined with "Conformally invariant energies of knots I" (math/0409396) to be "Conformally invariant energies of knots" which has replaced the former.

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This paper has been withdrawn by the authors; replaced by arXiv:0705.2531v2 [quant-ph].