The Quantum Links of the Anyons and their Entanglement

Abstract

In this paper, after a brief presentation of the physical 2+1 dimensional place where the anyons evolve, there is established the links creation probability for the anyons. The departure point is the celebrated Laughlin wave function. Then, two cases of quantum links are emphasized, considering two and three anyons. In the first case a two qubits register is attached. The unitary transformation (e.g. the UCNOT unitary transformation) can map not-entangled quantum states to the quantum and topological entangled states, as there are highlighted in this paper for the two anyons link case. The six qubit register which is attached to the three anyons link is only shortly presented since it represents a work in progress. The topologic and quantum states are represented by ket vectors and correspondingly by diagrams.