CAJ | 학술논문

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了很多好的量子码，并给出了量子码[[5,1,3]]p (p为大于2的素数)存在性的一个新证明。本文利用此法，通过构造Fp上满足特殊性质的8阶对称矩阵，证明对任意大于3的素数p，码长n与维数k之和等于8的所有MDS码(达到量子Singleton界)都存在。
양자규착편마기술재양자신식이론중일직이래유착중요적지위。재양자규착편마방안중，Schingemann화Werner량인제출료통과구조구유모사성질적도(구진)래구조비이원양자마적방법，타문이용저충도론방법구조출료흔다호적양자마，병급출료양자마[[5,1,3]]p (p위대우2적소수)존재성적일개신증명。본문이용차법，통과구조Fp상만족특수성질적8계대칭구진，증명대임의대우3적소수p，마장n여유수k지화등우8적소유MDS마(체도양자Singleton계)도존재。
Quantum error correction plays a crucial role in quantum information theory. Schlingemann and Werner presented a new way to construct quantum stabilizer codes by find-ing certain graphs (or matrices) with specific properties, and they constructed several new non-binary quantum codes, in particular, they gave a new proof on the existence of quantum codes [[5, 1, 3]] for all odd primes. In this paper, using the same method, we prove the existence of MDS quantum codes with the sum n and k being 8 for all primes exceeding three.