Topological quantum gate entanglers for a multi-qubit state

Abstract

We establish a relation between topological and quantum entanglement for a multi-qubit state by considering the unitary representations of the Artin braid group. We construct topological operators that can entangle a multi-qubit state. In particular we construct operators that create quantum entanglement for multi-qubit states based on the Segre ideal of complex multi-projective space. We also discuss in detail and construct these operators for two-qubit and three-qubit states.