A Boolean Functions Theoretic Approach to Quantum Hypergraph States and Entanglement
Abstract
The hypergraph states are pure multipartite quantum states corresponding to a hypergraph. It is an equal superposition of the states belonging to the computational basis. Given any hypergraph, we can construct a hypergraph state determined by a Boolean function. In contrast, we can find a hypergraph, corresponding to a Boolean function. This investigation develops a number of combinatorial structures concerned with the hypergraph states. For instance, the elements of the computational basis generate a lattice. The chains and antichains in this lattice assist us to find the equation of the Boolean function explicitly as well as to find a hypergraph. In addition, we investigate the entanglement property of the hypergraph states in terms of their combinatorial structures. We demonstrate several classes of hypergraphs, such that every cut of equal length on the corresponding hypergraph states has an equal amount of entanglement.
 Publication:

arXiv eprints
 Pub Date:
 November 2018
 DOI:
 10.48550/arXiv.1811.00308
 arXiv:
 arXiv:1811.00308
 Bibcode:
 2018arXiv181100308D
 Keywords:

 Mathematics  Combinatorics;
 Computer Science  Discrete Mathematics;
 Mathematical Physics;
 Quantum Physics
 EPrint:
 Comments are welcome