{"paper":{"title":"Quantum coherence generating power, maximally abelian subalgebras, and Grassmannian Geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Lorenzo Campos Venuti, Paolo Zanardi","submitted_at":"2017-06-23T21:37:55Z","abstract_excerpt":"We establish a direct connection between the power of a unitary map in $d$-dimensions ($d<\\infty$) to generate quantum coherence and the geometry of the set ${\\cal M}_d$ of maximally abelian subalgebras (of the quantum system full operator algebra). This set can be seen as a topologically non-trivial subset of the Grassmannian over linear operators. The natural distance over the Grassmannian induces a metric structure on ${\\cal M}_d$ which quantifies the lack of commutativity between the pairs of subalgebras. Given a maximally abelian subalgebra one can define, on physical grounds, an associat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07872","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"}