Polar codes for degradable quantum channels
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Bibliographic record
Abstract
Channel polarization is a phenomenon in which a particular recursive encoding induces a set of synthesized channels from many instances of a memoryless channel, such that a fraction of the synthesized channels becomes near perfect for data transmission and the other fraction becomes near useless for this task. Mahdavifar and Vardy have recently exploited this phenomenon to construct codes that achieve the symmetric private capacity for private data transmission over a degraded wiretap channel. In this paper, we build on their work and demonstrate how to construct quantum wiretap polar codes that achieve the symmetric private capacity of a degraded quantum wiretap channel with a classical eavesdropper. Due to the Schumacher-Westmoreland correspondence between quantum privacy and quantum coherence, we can construct quantum polar codes by operating these quantum wiretap polar codes in superposition, much like Devetak's technique for demonstrating the achievability of the coherent information rate for quantum data transmission. Our scheme achieves the symmetric coherent information rate for quantum channels that are degradable with a classical environment. This condition on the environment may seem restrictive, but we show that many quantum channels satisfy this criterion, including amplitude damping channels, photon-detected jump channels, dephasing channels, erasure channels, and cloning channels. Our quantum polar coding scheme has the desirable properties of being channel-adapted and symmetric capacity-achieving along with having an efficient encoder, but we have not demonstrated that the decoding is efficient. Also, the scheme may require entanglement assistance, but we show that the rate of entanglement consumption vanishes in the limit of large blocklength if the channel is degradable with classical environment. © 2012 IEEE.
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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 | 0.000 |
| 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 it