Additive Bounds of Minimum Output Entropies for Unital Channels and an Exact Qubit Formula
Bibliographic record
Abstract
We find an upper bound for the minimum output entropy of a unital quantum channel, and obtain an exact formula for general qubit channels. Our techniques incorporate the Rényi entropies, particularly, with Rényi parameter α = 2. Moreover, since our upper bound is additive under tensor product, we get as a corollary an upper bound for the classical capacity of unital quantum channels. Interestingly, our upper bound for the classical capacity depends only on the operator norm of matrix representations of channels on the space of traceless Hermitian operators, and is tight in the sense that it gives the precise quantity of classical capacity of the Werner-Holevo channel. As an example, we study quantum channels with operator sum representation that is made of the discrete Weyl operators (generalized Pauli operators), and explain how our formula works in this case. Finally, we find new examples for which the minimum output Rényi 2-entropy is additive.
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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 | 0.003 | 0.013 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.008 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.001 | 0.004 |
| Insufficient payload (model declined to judge) | 0.007 | 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".