{"paper":{"title":"Linear preservers and quantum information science","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"quant-ph","authors_text":"Ajda Fosner, Chi-Kwong Li, Nung-sing Sze, Zejun Huang","submitted_at":"2012-08-06T03:24:17Z","abstract_excerpt":"Let $m,n\\ge 2$ be positive integers, $M_m$ the set of $m\\times m$ complex matrices and $M_n$ the set of $n\\times n$ complex matrices. Regard $M_{mn}$ as the tensor space $M_m\\otimes M_n$. Suppose $|\\cdot|$ is the Ky Fan $k$-norm with $1 \\le k \\le mn$, or the Schatten $p$-norm with $1 \\le p \\le \\infty$ ($p\\ne 2$) on $M_{mn}$. It is shown that a linear map $\\phi: M_{mn} \\rightarrow M_{mn}$ satisfying $$|A\\otimes B| = |\\phi(A\\otimes B)|$$ for all $A \\in M_m$ and $B \\in M_n$ if and only if there are unitary $U, V \\in M_{mn}$ such that $\\phi$ has the form $A\\otimes B \\mapsto U(\\varphi_1(A) \\otimes "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1076","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"}