A Direct Product Theorem for Quantum Communication Complexity with Applications to Device-Independent Cryptography
Bibliographic record
Abstract
Abstract. We give a direct product theorem for the entanglement-assisted interactive quantum communication complexity of an [Formula: see text]-player predicate [Formula: see text]. In particular, we show that for a distribution [Formula: see text] that is product across the input sets of the [Formula: see text] players, the success probability of any entanglement-assisted quantum communication protocol for computing [Formula: see text] copies of [Formula: see text], whose communication is [Formula: see text], goes down exponentially in [Formula: see text]. Here [Formula: see text] is a distributional version of the quantum efficiency or partition bound introduced in [S. Laplante, V. Lerays, and J. Roland, Classical and quantum partition bound and detector inefficiency, in Automata, Languages, and Programming, Springer, Berlin, Heidelberg, 2012, pp. 617–628], which is a lower bound on the distributional quantum communication complexity of computing a single copy of [Formula: see text] with respect to [Formula: see text]. Applying our direct product theorem for small communication, and techniques related to [Formula: see text], we show that it is possible to do device-independent (DI) quantum cryptography without the assumption that devices do not leak any information. We analyze parallel and sequential versions of the DI quantum key distribution protocol given in [R. Jain, C. A. Miller, and Y. Shi [ IEEE Trans. Inform. Theory, 66 (2020), pp. 5567–5584], and show that it is possible to extract [Formula: see text] bits of key from it, even in the presence of [Formula: see text] bits of leakage. Finally, we show that proofs of quantumness with two entangled provers are resistant to leakage, i.e., classical players who communicate [Formula: see text] bits with each other cannot convince the verifier that they share entanglement.
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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 | 0.003 | 0.011 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.002 | 0.007 |
| Scholarly communication | 0.004 | 0.015 |
| Open science | 0.003 | 0.006 |
| Research integrity | 0.003 | 0.009 |
| Insufficient payload (model declined to judge) | 0.013 | 0.003 |
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".