Incompressibility of Classical Distributions
Bibliographic record
Abstract
Inblindcompression of quantum states, a sender Alice is given a specimen of a quantum state$\rho $drawn from a known ensemble (but without knowing what$\rho $is), and she transmits sufficient quantum data to a receiver Bob so that he can decode a near perfect specimen of$\rho $. For many such states drawn iid from the ensemble, the asymptotically achievable rate is the number of qubits required to be transmitted per state. The Holevo information is a lower bound for the achievable rate, and is attained for pure state ensembles, or in the related scenario of entanglement-assistedvisiblecompression of mixed states wherein Alice knows what state is drawn. In this paper, we prove a general and robust lower bound on the achievable rate for ensembles of classical states, which holds even in the least demanding setting when Alice and Bob share free entanglement and a constant per-copy error is allowed. We apply the bound to aspecificensemble of only two states and prove a near-maximal separation (saturating the dimension bound in leading order) between the best achievable rate and the Holevo information for constant error. This also implies that the ensemble is incompressible – compression does not reduce the communication cost by much. Since the states areclassical, the observed incompressibility is not fundamentally quantum mechanical. We lower bound the difference between the achievable rate and the Holevo information in terms of quantitative limitations to clone the specimen or to distinguish the two classical states.
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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 | 0.005 | 0.034 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.002 | 0.007 |
| Scholarly communication | 0.005 | 0.011 |
| Open science | 0.002 | 0.005 |
| Research integrity | 0.002 | 0.006 |
| Insufficient payload (model declined to judge) | 0.017 | 0.002 |
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".