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We study a finite-time cyclic copy protocol that creates persistingcorrelations between a memory and a data bit. The average work to copy the twostates of the data bit consists of the mutual information created between thememory and data bit after copying, a cost due to the difference between theinitial and final states of the memory bit, and a finite-time cost. At low copyspeeds, the optimal initial distribution of the memory bit matches the bias inthe expected outcome, set by the bias in the data bit and the copyingaccuracies. However, if both states of the data are copied with the sameaccuracy, then in the high-speed regime copying the unlikely data bit statebecomes prohibitively costly with a biased memory; the optimal initialdistribution is then pushed towards 50:50. Copying with unequal accuracies, atfixed copy-generated mutual information, yields an opposite yet more effectivestrategy. Here, the initial memory distribution becomes increasingly biased asthe copy speed increases, drastically lowering the work and raising the maximumspeed. This strategy is so effective that it induces a symmetry breakingtransition for an unbiased data bit.

Exploiting bias in optimal finite-time copying protocols