Efficient Quantum Polar Codes Requiring No Preshared Entanglement
arXiv:1307.1136 · doi:10.1109/TIT.2015.2468084
Abstract
We construct an explicit quantum coding scheme which achieves a communication rate not less than the coherent information when used to transmit quantum information over a noisy quantum channel. For Pauli and erasure channels we also present efficient encoding and decoding algorithms for this communication scheme based on polar codes (essentially linear in the blocklength), but which do not require the sender and receiver to share any entanglement before the protocol begins. Due to the existence of degeneracies in the involved error-correcting codes it is indeed possible that the rate of the scheme exceeds the coherent information. We provide a simple criterion which indicates such performance. Finally we discuss how the scheme can be used for secret key distillation as well as private channel coding.
very welcome! 35 pages, 10 figures. v2: Improvements to presentation. v3: published version
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Cited by in corpus (10)
- Entropic Uncertainty Relations and their Applications
- Quantum-memory-assisted entropic uncertainty relations
- Polar Codes and Their Quantum-Domain Counterparts
- Duality of channels and codes
- Entanglement-assisted concatenated quantum codes
- Coherent-state constellations and polar codes for thermal Gaussian channels
- Bounds on Information Combining With Quantum Side Information
- Alignment of Polarized Sets
- Partially Concatenated Calderbank-Shor-Steane Codes Achieving the Quantum Gilbert-Varshamov Bound Asymptotically
- Polar Codes for Quantum Reading