Generalized Tsirelson Inequalities, Commuting-Operator Provers, and Multi-prover Interactive Proof Systems
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
A central question in quantum information theory and computational complexity is how powerful nonlocal strategies are in cooperative games with imperfect information, such as multi-prover interactive proof systems. This paper develops a new method for proving limits of nonlocal strategies that make use of prior entanglement among players (or, provers, in the terminology of multi-prover interactive proofs). Instead of proving the limits for usual isolated provers who initially share entanglement, this paper proves the limits for "commuting-operator provers", who share private space, but can apply only such operators that are commutative with any operator applied by other provers. Obviously, these commuting-operator provers are at least as powerful as usual isolated but prior-entangled provers, and thus, limits in the model with commuting-operator provers immediately give limits in the usual model with prior-entangled provers. Using this method, we obtain an n-party generalization of the Tsirelson bound for the Clauser-Horne-Shimony-Holt inequality, for every n. Our bounds are tight in the sense that, in every n-party case, the equality is achievable by a usual nonlocal strategy with prior entanglement. We also apply our method to a three-prover one-round binary interactive proof system for NEXP. Combined with the technique developed by Kempe, Kobayashi, Matsumoto, Toner and Vidick to analyze the soundness of the proof system, it is proved to be NP-hard to distinguish whether the entangled value of a three-prover one-round binary-answer game is equal to one or at most 1-1/p(n) for some polynomial p, where n is the number of questions. This is in contrast to the two-prover one-round binary-answer case, where the corresponding problem is efficiently decidable. Alternatively, NEXP has a three-prover one-round binary interactive proof system with perfect completeness and soundness 1 middot 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-poly</sup> .
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 |
| 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 it