{"paper":{"title":"Channel capacities via $p$-summing norms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA","quant-ph"],"primary_cat":"math.FA","authors_text":"Carlos Palazuelos, Marius Junge","submitted_at":"2013-05-05T15:24:33Z","abstract_excerpt":"In this paper we show how \\emph{the metric theory of tensor products} developed by Grothendieck perfectly fits in the study of channel capacities, a central topic in \\emph{Shannon's information theory}. Furthermore, in the last years Shannon's theory has been generalized to the quantum setting to let the \\emph{quantum information theory} step in. In this paper we consider the classical capacity of quantum channels with restricted assisted entanglement. In particular these capacities include the classical capacity and the unlimited entanglement-assisted classical capacity of a quantum channel. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1020","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"}