The Sample Complexity of Quantum Entanglement Allocation
Abstract
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.
Related
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BibTeX
@misc{roll2026sample,
title = {{The Sample Complexity of Quantum Entanglement Allocation}},
author = {Nathan Roll},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10141},
eprint = {2609.10141},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10141},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Sample Complexity of Quantum Entanglement Allocation
AU - Nathan Roll
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10141
UR - https://arxiv.org/abs/2609.10141
AB - 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.
ER -