The Quantum Links of the Anyons and their Entanglement

TL;DR

This paper explores the formation of quantum links among anyons in a 2+1 dimensional setting, analyzing entanglement creation through unitary transformations and illustrating the topological and quantum states involved.

Contribution

It introduces a method to analyze quantum and topological entanglement of anyons using wave functions and unitary transformations, focusing on two and three anyon cases.

Findings

Unitary transformations can generate entangled states from unentangled ones.

Quantum links depend on the creation probability derived from the Laughlin wave function.

Preliminary analysis of three anyon links with a six-qubit register is presented.

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.