Constant gap between conventional strategies and those based on C*-dynamics for self-embezzlement
Bibliographic record
Abstract
We consider a bipartite transformation that we call self-embezzlement and use it to prove a constant gap between the capabilities of two models of quantum information: the conventional model, where bipartite systems are represented by tensor products of Hilbert spaces; and a natural model of quantum information processing for abstract states on C*-algebras, where joint systems are represented by tensor products of C*-algebras. We call this the C*-circuit model and show that it is a special case of the commuting-operator model (in that it can be translated into such a model). For the conventional model, we show that there exists a constant <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>&#x03F5;</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>&#x003E;</mml:mo><mml:mn>0</mml:mn></mml:math> such that self-embezzlement cannot be achieved with precision parameter less than <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>&#x03F5;</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math> (i.e., the fidelity cannot be greater than <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>&#x03F5;</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math>); whereas, in the C*-circuit model---as well as in a commuting-operator model---the precision can be <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>0</mml:mn></mml:math> (i.e., fidelity <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>1</mml:mn></mml:math>).Self-embezzlement is not a non-local game, hence our results do not impact the celebrated Connes Embedding conjecture. Instead, the significance of these results is to exhibit a reasonably natural quantum information processing problem for which there is a constant gap between the capabilities of the conventional Hilbert space model and the commuting-operator or C*-circuit model.
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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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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".