2011/09/30 by Joseph M. Renes, Frédéric Dupuis, Frederic Dupuis +1 · 2 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Binary erasure channel #Block code #Channel (broadcasting) #Channel capacity #Coding (social sciences) #Combinatorics #Computer science #DNA and Biological Computing #Decoding methods #Error Correcting Code Techniques #Mathematics #Physics #Polar code #Quantum #Quantum Computing Algorithms and Architecture #Quantum channel #Quantum entanglement #Quantum information #Quantum mechanics #Qubit #Superdense coding #Telecommunications #Theoretical computer science #Topology (electrical circuits) #cs.IT #math.IT #quant-ph
paper · pdf · doi:10.1103/physrevlett.109.050504
published as Phys. Rev. Lett. 109, 050504 (2012) · v1: 15 pages, 4 figures. v2: 5+3 pages, 3 figures; argumentation simplified and improved
arxiv created 2012/03/24 · openalex publication_date 2012/08/01 · arxiv updated 2012/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Polar coding, introduced 2008 by Arıkan, is the first (very) efficiently encodable and decodable coding scheme whose information transmission rate provably achieves the Shannon bound for classical discrete memoryless channels in the asymptotic limit of large block sizes. Here, we study the use of polar codes for the transmission of quantum information. Focusing on the case of qubit Pauli channels and qubit erasure channels, we use classical polar codes to construct a coding scheme that asymptotically achieves a net transmission rate equal to the coherent information using efficient encoding and decoding operations and code construction. Our codes generally require preshared entanglement between sender and receiver, but for channels with a sufficiently low noise level we demonstrate that the rate of preshared entanglement required is zero.