Recursive encoding and decoding of the noiseless subsystem for qudits
Utkan Güngördü, Chi-Kwong Li, Mikio Nakahara, Yiu‐Tung Poon, Nung-Sing Sze · Physical Review A · 2014
We give a full explanation of the noiseless subsystem that protects a single qubit against collective errors and the corresponding recursive scheme described by C.-K. Li et al. [Phys. Rev. A 84, 044301 (2011)] from a representation theory point of view. Furthermore, we extend the construction to qudits under the influence of collective SU($d$) errors. We find that under this recursive scheme, the asymptotic encoding rate is $1/d$.