Study Of Additive Quantum Codes Based On Quotient Space

In recent years,quantum information science has flourished as an emerging in-terdisciplinary subject of physics,information science and mathematics is expected to cause a revolutionary change in information science.Due to the special commu-nication mechanism of quantum physics,the problem of quantum error correction is much difficult and more important than that of classical communication.The quantum error correction has become one of the key problems for the realization of quantum information.Among many quantum error correction codes theories,the additive quantum codes is an important method for quantum error correction coding,in which an in-variant subspace of a commutative subgroup of the quantum error operator group is used to construct a quantum code.However,it seems too wasteful to use only one invariant subspace to construct a quantum code.This article studies the use of multiple invariant subspaces of commutative subgroups to construct a quantum code.Since each invariant subspace can be described by an equivalence class in the quotient space,the theory of quotient space can be used to study the construction of multiple invariant subspace quantum codes.Based on this idea,this thesis estab-lishes the quotient space code and gives its corresponding code bound by analogy with the classical error correction codes.Under the framework of the quotient space codes,this thesis successfully solves the construction problem of multiple invari-ant subspace quantum codes,and after combining the quaternion codes construction method,this thesis not only verifies the code bound of quantum codes,proves that constructing perfect quantum codes and quantum MDS codes can by finding per-fect quotient space codes and MDS quotient space codes,but also presents a GV bound of multiple invariant subspace additive quantum codes.In addition,this the-sis applies the quotient space code construction method to the study of asymmetric additive quantum codes.The author believes that quotient space codes construction method will be a good tool in other studies of additive quantum codes.