= Asymptotic remote state preparation by block indexing
{title2=$\mathbb E L/n\longrightarrow1$}
Prepare independent candidate blocks by <one-bit heralding of a remote state preparation block>, but send only the first successful block's index. Success eventually occurs with <probability> one; a <prefix code for a rare geometric success> uses at most $n+e/(e-1)$ expected <bits> per block. The expected <singlet state> consumption is $n2^n$. Alternatively, limiting the number of trials to $n2^n$ gives failure <probability> at most $e^{-n}$ and a fixed message length $n+\log_2n+O(1)$. Both versions approach one classical <bit> per remotely prepared <qubit> in their respective expected-length or high-success senses.
// Target: quantum-theory.bigb
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