From Holant to Quantum Entanglement and Back
Abstract
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 ${\Psi_6}\rangle$ of 6 qubits and ${\Psi_8}\rangle$ of 8 qubits respectively, that have extraordinary and unique closure properties in terms of the Bell property. Then we use entanglement properties of constraint functions to derive a new complexity dichotomy for all realvalued Holant problems containing an oddarity signature. The signatures need not be symmetric, and no auxiliary signatures are assumed.
 Publication:

arXiv eprints
 Pub Date:
 April 2020
 DOI:
 10.48550/arXiv.2004.05706
 arXiv:
 arXiv:2004.05706
 Bibcode:
 2020arXiv200405706C
 Keywords:

 Computer Science  Computational Complexity;
 Quantum Physics
 EPrint:
 46 pages