How many past requests are needed to decide which qubits should share entanglement? We show that the answer depends on the allocation choices created by the queries: a larger memory can require no more data. The memory stores a classical bit and answers requests through a fixed detector that preserves coherence within each measured sector. For independent commuting
X- and
Z-type Pauli queries, we characterize the full attainable prediction-contrast region and construct encodings that preserve the bit at every nonzero vertex. With sharp reports, a
d-qubit path and groups of at most
k qubits have minimax excess error after
m requests proportional to
k−1min{1,dlog(k+1)/m}, uniformly for
2≤k<d. Connected biclique regions can grow without increasing sample demand when depth, region count and connections per region stay bounded. Preparation noise introduces a separate calibration requirement. We derive an exact tradeoff with extra fresh detector calls and transfer the learning law to structured transaction co-location. Population-risk experiments test the statistical predictions. We also compare encodings on a native 15-qubit device and learned partitions on public purchase baskets. The full chain wins on the device; frequency grouping outperforms basket search in the largest-capacity retail setting.