Bibliographic record
Abstract
Holevo, Schumacher, and Westmoreland's coding theorem guarantees the existence of codes that are capacity-achieving for the task of sending classical data over a channel with classical inputs and quantum outputs. Although they demonstrated the existence of such codes, their proof does not provide an explicit construction of codes for this task. The aim of this paper is to fill this gap by constructing near-explicit “polar” codes that are capacity-achieving. The codes exploit the channel polarization phenomenon observed by Arikan for the case of classical channels. Channel polarization is an effect in which one can synthesize a set of channels, by “channel combining” and “channel splitting,” in which a fraction of the synthesized channels are perfect for data transmission, while the other channels are completely useless for data transmission, with the good fraction equal to the capacity of the channel. The channel polarization effect then leads to a simple scheme for data transmission: send the information bits through the perfect channels and “frozen” bits through the useless ones. The main technical contributions of this paper are threefold. First, we leverage several known results from the quantum information literature to demonstrate that the channel polarization effect occurs for channels with classical inputs and quantum outputs. We then construct linear polar codes based on this effect, and the encoding complexity isO(NlogN), whereNis the blocklength of the code. We also demonstrate that a quantum successive cancellation decoder works well, in the sense that the word error rate decays exponentially with the blocklength of the code. For this last result, we exploit Sen's recent “noncommutative union bound” that holds for a sequence of projectors applied to a quantum state.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.000 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".