Recursive encoding and decoding of the noiseless subsystem for qudits

Abstract

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 $1/d$.

References in corpus (4)

• Quantum Error Correction
• A numerical algorithm for the explicit calculation of SU(N) and SL(N,C) Clebsch-Gordan coefficients
• Recursive Encoding and Decoding of Noiseless Subsystem and Decoherence Free Subspace
• Quantum Error Correction with Uniformly Mixed State Ancillae