{"corpus_id":44232418,"paper_sha":"b837dace56c78408d1726edb04d8b3df14f03c16","doi":"10.1103/PhysRevA.63.050301","arxiv_id":"quant-ph/0009109","pmid":null,"pmcid":null,"mag_id":1982683415,"dblp_id":null,"acl_id":null,"title":"Schmidt number witnesses and bound entanglement","year":2000,"publication_date":"2000-09-26","venue":"","journal":{"name":"Physical Review A","pages":"050301","volume":"63"},"journal_issn":null,"journal_title":null,"publication_types":[],"pubmed_pub_types":null,"s2_fields_of_study":["Physics"],"reference_count":4,"citation_count":189,"influential_citation_count":8,"is_open_access":true,"arxiv_categories":["quant-ph"],"arxiv_license":null,"arxiv_journal_ref":"Phys. Rev. A 63, 050301 (2001)","mesh_headings":null,"chemicals":null,"comments_corrections":null,"source_flags":1,"s2_open_access_pdf_url":"https://arxiv.org/pdf/quant-ph/0009109","s2_open_access_landing_url":"https://www.semanticscholar.org/paper/b837dace56c78408d1726edb04d8b3df14f03c16","s2_open_access_license":null,"s2_open_access_status":"GREEN","pmc_open_access_pdf_url":null,"pmc_open_access_landing_url":null,"pmc_open_access_license":null,"pmc_open_access_status":null,"unpaywall_open_access_pdf_url":null,"unpaywall_open_access_landing_url":null,"unpaywall_open_access_license":null,"unpaywall_open_access_status":null,"abstract":"The Schmidt number of a mixed state characterizes the minimum Schmidt rank of the pure states needed to construct it. We investigate the Schmidt number of an arbitrary mixed state by studying Schmidt-number witnesses that detect it. We present a canonical form of such witnesses and provide constructive methods for their optimization. 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