1999/06/30 by A. Ashikhmin, Alexei Ashikhmin, A. Barg +9
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum-Dot Cellular Automata #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/9906131
arxiv created 1999/06/30 · openalex publication_date 1999/06/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In Part II we show that there exist quantum codes whose probability of undetected error falls exponentially with the length of the code and derive bounds on this exponent.The lower (existence) bound for stabilizer codes is proved by a counting argument for classical self-orthogonal quaternary codes. Upper bounds for any quantum codes are proved by linear programming. We present two general solutions of the LP problem. Together they give an upper bound on the exponent of undetected error. The upper and lower asymptotic bounds coincide for a certain interval of code rates close to 1.