受李代数启发的量子信息的加权图论表示
Weighted Graph Theory Representation of Quantum Information Inspired by Lie Algebras
摘要：
借鉴单缀层李代数与Dynkin图之间的关系，提出了量子信息的加权图论表示。这样，一个量子态的密度矩阵可以被解释为一个关联图的无符号拉普拉斯矩阵。利用单缀层李代数与根系的相似性，对单量子比特理论进行了详细的分析，发现它与一个具有两个顶点的无向加权图有关。此外，这种单量子比特理论被推广到n量子比特。在该表示中，量子门对应于保持概率条件的图权重操作。从弦论，通过D-膜颤动，也给出了一个猜测。
英文摘要：
Borrowing ideas from the relation between simply laced Lie algebras and Dynkin diagrams, a weighted graph theory representation of quantum information is addressed. In this way, the density matrix of a quantum state can be interpreted as a signless Laplacian matrix of an associated graph. Using similarities with root systems of simply laced Lie algebras, one-qubit theory is analyzed in some details and is found to be linked to a non-oriented weighted graph having two vertices. Moreover, this one-qubit theory is generalized to n-qubits. In this representation, quantum gates correspond to graph weight operations preserving the probability condition. A speculation from string theory, via D-brane quivers, is also given.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
