  We study a finite-time cyclic copy protocol that creates persisting
correlations between a memory and a data bit. The average work to copy the two
states of the data bit consists of the mutual information created between the
memory and data bit after copying, a cost due to the difference between the
initial and final states of the memory bit, and a finite-time cost. At low copy
speeds, the optimal initial distribution of the memory bit matches the bias in
the expected outcome, set by the bias in the data bit and the copying
accuracies. However, if both states of the data are copied with the same
accuracy, then in the high-speed regime copying the unlikely data bit state
becomes prohibitively costly with a biased memory; the optimal initial
distribution is then pushed towards 50:50. Copying with unequal accuracies, at
fixed copy-generated mutual information, yields an opposite yet more effective
strategy. Here, the initial memory distribution becomes increasingly biased as
the copy speed increases, drastically lowering the work and raising the maximum
speed. This strategy is so effective that it induces a symmetry breaking
transition for an unbiased data bit.
