发表机构
Tikhonov Moscow Institute of Electronics and Mathematics, HSE University（季霍诺夫莫斯科电子与数学研究所，高等经济大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究对比纯qudit态的马约拉纳表示与广义布洛赫表示，推导两者间的解析关系，还分析其在对称多量子比特态的扩展，为研究两量子比特态的量子关联提供几何视角。
AI 中文摘要
布洛赫球为量子比特提供了标准几何表示，但其向纯qudit态（d>2）的推广并非唯一。该表示可通过两种不同方法扩展：一是增加点数，如马约拉纳表示；二是使用单个点但在更高维空间中，如广义布洛赫表示。本研究通过寻找两者间的显式解析关系，对比了纯qudit态的这些表示，特别给出了由给定态的马约拉纳点表示布洛赫矢量的通用公式，还分析了纯置换对称两量子比特和三量子比特态下这些表示的合适扩展，推导了对应关系。这些解析结果使我们能从几何视角研究特殊类两量子比特态的量子关联。
英文摘要
While the Bloch sphere provides a canonical geometric representation for qubits, its generalization to pure qudit states ($d>2$) is not unique. This representation can be extended following two different approaches: increasing the number of points, as in the Majorana representation, or using a single point but in a space of larger dimension, as in the generalized Bloch representation. In this work, we compare these representations of pure qudit states by finding explicit analytical relations between them. In particular, a general formula of the Bloch vector in terms of the Majorana points of a given state is provided. We also analyze some suitable extensions of these representations in the case of pure permutation-symmetric two- and three-qubit states, deriving the corresponding relation between them. These analytical results allow us to study, from a geometric point of view, quantum correlations of special classes of two-qubit states.
Comments20 pages
