Maximal noiseless code rates for collective rotation channels on qudits

Chi Kwong Li, Mikio Nakahara, Yiu Tung Poon, Nung Sing Sze

Research output: Journal article publicationJournal articleAcademic researchpeer-review


We study noiseless subsystems on collective rotation channels of qudits, i.e., quantum channels with operators in the set ε(d,n)= {U⊗n : U ∈ SU(d)}. This is done by analyzing the decomposition of the algebra A(d,n) generated by ε(d,n). We summarize the results for the channels on qubits (d=2) and obtain the maximum dimension of the noiseless subsystem that can be used as the quantum error correction code for the channel. Then we extend our results to general d. In particular, it is shown that the code rate, i.e., the number of protected qudits over the number of physical qudits, always approaches 1 for a suitable noiseless subsystem. Moreover, one can determine the maximum dimension of the noiseless subsystem by solving a non-trivial discrete optimization problem. The maximum dimension of the noiseless subsystem for d=3 (qutrits) is explicitly determined by a combination of mathematical analysis and the symbolic software Mathematica.
Original languageEnglish
Pages (from-to)4039-4055
Number of pages17
JournalQuantum Information Processing
Issue number11
Publication statusPublished - 1 Nov 2015


  • Irreducible representations
  • Quantum error correction
  • Qudits
  • Special unitary groups

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Theoretical Computer Science
  • Electronic, Optical and Magnetic Materials
  • Signal Processing
  • Modelling and Simulation
  • Electrical and Electronic Engineering

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