The Fractional Statistical Properties And The Application In Quantum Information Of Anyons

Anyon is one kind of two-dimensional quasiparticle with fantanstic properties. Different from bosons and fermions, anyons obey fractional statistics which leads to many interesting phenomena. Recently these phenomena have been observed in many experiments. Because of these phonomena, anyons play an important role in many fields of physics, especially, in the field of quantum information.This paper was consisted of four parts: the relationship between the properties of Gentile statistics and fractional statistics of anyon; some basic problems of quantum information; a protocol to simulate quantum gates using abelian anyons; and the construction of decoherence-free subspaces of anyon states.In the part of the relationship between the properties of Gentile statistics and fractional statistics of anyons is studied. The winding number representation of anyons is introduced to realize the transformation between anyon statistics and Gentile statistics. Under the winding number representation, the quantum intermediate statistical braket and the coherent state of anyon are discussed, and the properties of anyons are simulated by Gentile statistics with a geometric phase.In the second part, we discuss two fundamental problems in quantum information: why classical information can be copied and the difference between quantum and classical deletion.In the following part, a protocol to simulate quantum gates using abelian anyons was proposed. Moreover, single qubit quantum gates and two qubits CNOT gate are simulated with Grover algorithm as an example.In the end, decoherence-free subspaces of anyon states were dicussed, as well as the forms of the noise are given. And again, the Kitaev model are used here as an example.