{"paper":{"title":"Group structures and representations of graph states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Dagmar Bru{\\ss}, Hermann Kampermann, Jun-Yi Wu","submitted_at":"2015-04-13T19:13:55Z","abstract_excerpt":"A special configuration of graph state stabilizers, which contains only Pauli $\\sigma_X$ operators, is studied. The vertex sets $\\xi$ associated with such configurations are defined as what we call X-chains of graph states. The X-chains of a general graph state can be determined efficiently. They form a group structure such that one can obtain the explicit representation of graph states in the X-basis via the so-called X-chain factorization diagram. We show that graph states with different X-chain groups can have different probability distributions of X-measurement outcomes, which allows one t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.03302","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"}