Operational interpretation of the Choi rank through exclusion tasks
Bibliographic record
Abstract
The Choi state is an indispensable tool in the study and analysis of quantum channels. Considering a channel in terms of its associated Choi state can greatly simplify problems. It also offers an alternative approach to the characterization of a channel, with properties of the Choi state providing novel insight into a channel's behavior. The rank of a Choi state, termed the Choi rank, has proven to be an important characterizing property, and here, its significance is further elucidated through an operational interpretation. The Choi rank is shown to provide a universal bound on how successfully two agents, Alice and Bob, can perform an entanglement-assisted exclusion task. The task can be considered an extension of superdense coding, where Bob can only output information about Alice's encoded bit string with certainty. Conclusive state exclusion, in place of state discrimination, is therefore considered at the culmination of the superdense coding protocol. In order to prove this result, a necessary condition for conclusive k -state exclusion of a set of states is presented in order to achieve this result, and the notions of weak and strong exclusion are introduced.
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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 | 0.007 | 0.017 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.002 | 0.012 |
| Scholarly communication | 0.005 | 0.012 |
| Open science | 0.002 | 0.007 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.005 | 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".