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 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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.004 | 0.004 |
| 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".