A Stabilizer Formalism for Infinitely Many Qubits
Bibliographic record
Abstract
The study of infinite dimensional quantum systems has been an active area of discussion in quantum information theory, particularly in settings where certain properties are shown to be not attainable by any finite dimensional system (such as nonlocal correlations). \nSimilarly, the notion of stabilizer states has yielded interesting developments in areas like error correction, efficient simulation of quantum systems and its relation to graph states. \nHowever, the commonly used model of tensor products of finite dimensional Hilbert spaces is not sufficiently general to capture infinite dimensional stabilizer states. \nA more general framework quantum mechanical systems using C*-algebras has been instrumental in studying systems with an infinite number of discrete systems in quantum statistical mechanics and quantum field theory. \nWe propose a framework in the C*-algebra model (specifically, the CAR algebra) for the stabilizer formalism that extends to infinitely many qubits. \nImportantly, the stabilizer states on the CAR algebra form a class of states that can attain unbounded entanglement and yet has a simple characterization through the group structure of its stabilizer. \nIn this framework, we develop a theory for the states, operations and measurements needed to study open questions in quantum information.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.006 | 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".