两个非对称图量子MDS码的构造

Construction of two asymmetric graph quantum MDS codes

量子纠错编码技术在量子信息理论中一直以来有着重要的地位,在量子纠错编码方案中,Schingemann和Werner两人提出了通过构造具有某些性质的图(矩阵)来构造非二元量子码的方法,他们利用这种图论方法构造出很多好的量子码,特别给出量子码[[5,1,3]]_p(p≥3)存在性的一个新证明。此方法可从对称量子码推广至非对称量子码的构造,利用推广方法证明了非对称图量子MDS码[[5,1,4/2]]p,(p>5)和[[7,1,6/2]]p(p>7)的存在性。

Quantum error correction plays a crucial role in quantum information theory.Schlingemann and Wernerpresented a new way to construct quantum stabilizer codes by finding certain graphs(or matrices)with specific properties,and they constructed several new nonbinary quantum codes by the way,in particular,they gave a new proof on existenceof quantum codes[[5,1,3]]p(p≥3).The way can be generalized the construction of symmetric quantum codes to theasymmetric case.Using this method,the existence of asymmetric graph quantum MDS codes with parameters[[5,1,4/2]]pand[[7,1,6/2]]p is showed separately for all primes p>5and p>7by graph machinery.