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Title: Maximal noiseless code rates for collective rotation channels on qudits
Authors: Li, CK
Nakahara, M
Poon, YT
Sze, NS 
Keywords: Irreducible representations
Quantum error correction
Special unitary groups
Issue Date: 2015
Publisher: Springer
Source: Quantum information processing, 2015, v. 14, no. 11, p. 4039-4055 How to cite?
Journal: Quantum information processing 
Abstract: 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.
ISSN: 1570-0755
DOI: 10.1007/s11128-015-1101-2
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