New One Shot Quantum Protocols With Application to Communication Complexity
Bibliographic record
Abstract
In this paper, we present the following quantum compression protocol `P': Let ρ,σ be quantum states, such that S (ρ∥σ) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">def</sup> = Tr(ρ log ρ - ρ log σ), the relative entropy between ρ and σ, is finite. Alice gets to know the eigendecomposition of ρ. Bob gets to know the eigendecomposition of σ. Both Alice and Bob know S(ρ∥σ) and an error parameter ε. Alice and Bob use shared entanglement and after communication of O((S(ρ∥σ) + 1)/ε <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> ) bits from Alice to Bob, Bob ends up with a quantum state ̃ρ̃, such that F(ρ, ρ̃) ≥ 1-5ε, where F(·) represents fidelity. This result can be considered as a non-commutative generalization of a result due to Braverman and Rao where they considered the special case when ρ and σ are classical probability distributions (or commute with each other) and use shared randomness instead of shared entanglement. We use? to obtain an alternate proof of a direct-sum result for entanglement assisted quantum one-way communication complexity for all relations, which was first shown by Jain et al.. We also present a variant of protocol? in which Bob has some side information about the state with Alice. We show that in such a case, the amount of communication can be further reduced, based on the side information that Bob has. Our second result provides a quantum analog of the widely used classical correlated-sampling protocol. For example, Holenstein used the classical correlated-sampling protocol in his proof of a parallel-repetition theorem for two-player one-round games.
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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 | 0.000 | 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 | 0.001 | 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 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".