Near-optimal bounds on bounded-round quantum communication complexity of\n disjointness
Bibliographic record
Abstract
We prove a near optimal round-communication tradeoff for the two-party\nquantum communication complexity of disjointness. For protocols with $r$\nrounds, we prove a lower bound of $\\tilde{\\Omega}(n/r + r)$ on the\ncommunication required for computing disjointness of input size $n$, which is\noptimal up to logarithmic factors. The previous best lower bound was\n$\\Omega(n/r^2 + r)$ due to Jain, Radhakrishnan and Sen [JRS03]. Along the way,\nwe develop several tools for quantum information complexity, one of which is a\nlower bound for quantum information complexity in terms of the generalized\ndiscrepancy method. As a corollary, we get that the quantum communication\ncomplexity of any boolean function $f$ is at most $2^{O(QIC(f))}$, where\n$QIC(f)$ is the prior-free quantum information complexity of $f$ (with error\n$1/3$).\n
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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 | 0.009 | 0.039 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.002 | 0.008 |
| Scholarly communication | 0.006 | 0.017 |
| Open science | 0.005 | 0.010 |
| Research integrity | 0.003 | 0.010 |
| Insufficient payload (model declined to judge) | 0.010 | 0.002 |
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".