{"paper":{"title":"On the Matrix Representation of Quantum Operations","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Kazuo Nakamura, Yoshihiro Nambu","submitted_at":"2005-04-12T11:40:46Z","abstract_excerpt":"This paper considers two frequently used matrix representations -- what we call the $\\chi$- and $\\mathcal{S}$-matrices -- of a quantum operation and their applications. The matrices defined with respect to an arbitrary operator basis, that is, the orthonormal basis for the space of linear operators on the state space are considered for a general operation acting on a single or two \\textit{d}-level quantum system (qudit). We show that the two matrices are given by the expansion coefficients of the Liouville superoperator as well as the associated bijective, positive operator on the doubled-spac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0504091","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/quant-ph/0504091/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}