{"paper":{"title":"Maximal noiseless code rates for collective rotation channels on qudits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Chi-Kwong Li, Mikio Nakahara, Nung-sing Sze, Yiu-Tung Poon","submitted_at":"2013-06-05T04:32:43Z","abstract_excerpt":"We study noiseless subsystems on collective rotation channels of qudits, i.e., quantum channels with operators in the set ${\\mathcal E}(d,n) = \\{ U^{\\otimes n}: U \\in {\\mathrm{SU}}(d)\\}.$ This is done by analyzing the decomposition of the algebra ${\\mathcal A}(d,n)$ generated by ${\\mathcal E}(d,n)$. 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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0981","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}