{"paper":{"title":"Projection methods in quantum information science","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Chi-Kwong Li, Diane Pelejo, Dmitriy Drusvyatskiy, Henry Wolkowicz, Yuen-Lam Cheung","submitted_at":"2014-07-24T14:50:19Z","abstract_excerpt":"We consider the problem of constructing quantum operations or channels, if they exist, that transform a given set of quantum states $\\{\\rho_1, \\dots, \\rho_k\\}$ to another such set $\\{\\hat\\rho_1, \\dots, \\hat\\rho_k\\}$. In other words, we must find a {\\em completely positive linear map}, if it exists, that maps a given set of density matrices to another given set of density matrices. This problem, in turn, is an instance of a positive semi-definite feasibility problem, but with highly structured constraints. The nature of the constraints makes projection based algorithms very appealing when the n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.6604","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":""},"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"}