{"paper":{"title":"Efficient Quantum Error Correction for Fully Correlated Noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Chi-Kwong Li, Hiroyuki Tomita, Mikio Nakahara, Nung-sing Sze, Yiu-Tung Poon","submitted_at":"2011-04-25T16:51:09Z","abstract_excerpt":"We investigate an efficient quantum error correction of a fully correlated noise. Suppose the noise is characterized by a quantum channel whose error operators take fully correlated forms given by $\\sigma_x^{\\otimes n}$, $\\sigma_y^{\\otimes n}$ and $\\sigma_z^{\\otimes n}$, where $n>2$ is the number of qubits encoding the codeword. It is proved that (i) $n$ qubits codeword encodes $(n-1)$ data qubits when $n$ is odd and (ii) $n$ qubits codeword implements a noiseless subsystem encoding $(n-2)$ data qubits when $n$ is even. Quantum circuits implementing these schemes are constructed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.4750","kind":"arxiv","version":2},"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"}