The Pauli channel acting on 2 x 2 matrices is generalized to an n-level quantum system. When the full matrix algebra M is decomposed into pairwise complementary subalgebras, then trace-preserving linear mappings from M to M are constructed such that the restriction to the subalgebras are depolarizing channels. The result is the necessary and sufficient condition of complete positivity. The main examples appear on bipartite systems
推广了D. S. Shirokov关于维数为$2^n$的实Clifford代数或复Clifford代数的两组反交换元的一个定理，推广到两组反交换元光滑依赖于维数为$r$的欧氏空间的点的情形.证明了在偶$n$情形下，存在一个光滑函数使得两个Clifford代数元素集通过相似变换连接.在奇$n$的情况下，考虑两个集合之间的连接的所有情况。利用一般形式的自旋联系方程，证明了局部泡利定理的问题等价于某些特殊的偏微分方程组的解的存在性问题。详细考虑了问题的特殊情况$n=2$，$r\geq 1$和具有更简单解的$n\geq 2$，$r=1$.
Capacity-Achieving Entanglement Purification Protocol for Pauli Dephasing Channel
The Australian National University（澳大利亚国立大学）；University of Queensland（昆士兰大学）；Commonwealth Scientific and Industrial Research Organisation（联邦科学与工业研究组织）；Agency for Science, Technology and Research (A*STAR)（科学技术研究局）
Efficient self-consistent learning of gate set Pauli noise
Pritzker School of Molecular Engineering, The University of Chicago（芝加哥大学普里茨克分子工程学院）；Institute for Interdisciplinary Information Sciences, Tsinghua University（清华大学交叉信息研究院）；Department of Computer Science, Virginia Tech（弗吉尼亚理工大学计算机科学系）；Phasecraft Inc.（Phasecraft公司）
