2005/06/30 by Shun Watanabe, Ryutaroh Matsumoto, Tomohiko Uyematsu
Computer Science · Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Class (philosophy) #Coding theory and cryptography #Distillation #Encoding (memory) #Equivalence (formal languages) #Equivalence class (music) #Mathematical Analysis and Transform Methods #quant-ph
paper · pdf · doi:10.1088/0305-4470/39/16/013
published as Journal of Physics A: Mathematical and General, vol.39, no.16, pp.4273--4290, March 2006 · 22 pages, 2 figures, In version 2, we enumerate all encoding operators in the Clifford group, and fix the wrong classification of encoding operators in version 1
arxiv created 2005/11/07 · openalex publication_date 2006/03/31 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
This paper presents a method for enumerating all encoding operators in the Clifford group for a given stabilizer. Furthermore, we classify encoding operators into the equivalence classes such that EDPs (Entanglement Distillation Protocol) constructed from encoding operators in the same equivalence class have the same performance. By this classification, for a given parameter, the number of candidates for good EDPs is significantly reduced. As a result, we find the best EDP among EDPs constructed from [[4,2]] stabilizer codes. This EDP has a better performance than previously known EDPs over wide range of fidelity.