A quantum Goldreich-Levin theorem with cryptographic applications
Bibliographic record
Abstract
We investigate the Goldreich-Levin Theorem in the context of quantum information. This result is a reduction from the computational problem of inverting a one-way function to the problem of predicting a particular bit associated with that function. We show that the quantum version of the reduction -- between quantum one-way functions and quantum hard-predicates -- is quantitatively more efficient than the known classical version. Roughly speaking, if the one-way function acts on n-bit strings then the overhead in the reduction is by a factor of O(n/epsilon^2) in the classical case but only by a factor of O(1/epsilon) in the quantum case, where 1/2 + epsilon is the probability of predicting the hard-predicate. Moreover, we prove via a lower bound that, in a black-box framework, the classical version of the reduction cannot have overhead less than order n/epsilon^2. We also show that, using this reduction, a quantum bit commitment scheme that is perfectly binding and computationally concealing can be obtained from any quantum one-way permutation. This complements a recent result by Dumais, Mayers and Salvail, where the bit commitment scheme is perfectly concealing and computationally binding. We also show how to perform qubit commitment by a similar approach.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| 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".