2026-07-24T18:10:37Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:12429 2024-03-06T10:50:07Z ddc:004 open_access

From Holant to Quantum Entanglement and Back Cai, Jin-Yi Fu, Zhiguo Shao, Shuai Holant problem Quantum entanglement SLOCC equivalence Bell property Holant problems are intimately connected with quantum theory as tensor networks. We first use techniques from Holant theory to derive new and improved results for quantum entanglement theory. We discover two particular entangled states |Ψ₆⟩ of 6 qubits and |Ψ₈⟩ of 8 qubits respectively, that have extraordinary closure properties in terms of the Bell property. Then we use entanglement properties of constraint functions to derive a new complexity dichotomy for all real-valued Holant problems containing a signature of odd arity. The signatures need not be symmetric, and no auxiliary signatures are assumed. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Jin-Yi Cai and Zhiguo Fu and Shuai Shao 2020 Is Part Of LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2020.22 urn:nbn:de:0030-drops-124298 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.22 eng https://creativecommons.org/licenses/by/3.0/legalcode