On the conditions for discrimination between quantum states with minimum error
Bibliographic record
Abstract
In quantum communications a transmitting party, Alice, selects from among a set of agreed quantum states to prepare a quantum system for transmission to the receiving party, Bob. Both the set of possible states, {ρˆi}, and the associated probabilities for selection, {pi}, are known to Bob but not, of course, the selected state. His task is to determine as well as he can which state was prepared and he does this by choosing a measurement to perform. If the states are not mutually orthogonal then there is no measurement that will reveal the selected state with certainty. The strategy he chooses will depend on the use for which the information is intended and there exist many figures of merit for Bob's measurement [1, 2]. Among these the simplest is the minimum probability of error or, equivalently, the maximum probability for correctly identifying the state. Necessary and sufficient conditions for realizing a minimum error measurement are known [3-6], but it has proven to be easier to prove sufficiency than necessity. This letter presents an appealingly simple proof that the conditions are necessary.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".