Quantum rate distortion, reverse shannon theorems, and source-channel separation
Bibliographic record
Abstract
We derive quantum counterparts of two key theorems of classical information theory, namely, the rate-distortion theorem and the source-channel separation theorem. The rate-distortion theorem gives the ultimate limits on lossy data compression, and the source-channel separation theorem implies that a two-stage protocol consisting of compression and channel coding is optimal for transmitting a memoryless source over a memoryless channel. In spite of their importance in the classical domain, there has been surprisingly little work in these areas for quantum information theory. In this paper, we prove that the quantum rate-distortion function is given in terms of the regularized entanglement of purification. We also determine a single-letter expression for the entanglement-assisted quantum rate-distortion function, and we prove that it serves as a lower bound on the unassisted quantum rate-distortion function. This implies that the unassisted quantum rate-distortion function is nonnegative and generally not equal to the coherent information between the source and distorted output (in spite of Barnum's conjecture that the coherent information would be relevant here). Moreover, we prove several quantum source-channel separation theorems. The strongest of these are in the entanglement-assisted setting, in which we establish a necessary and sufficient condition for transmitting a memoryless source over a memoryless quantum channel up to a given distortion. © 2012 IEEE.
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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 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.004 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".