Projective ring line of an arbitrary single qudit
Projective ring line of an arbitrary single qudit
复制标题
任意单个 Qudit 的投影环线
DOI：
10.1088/1751-8113/41/1/015302
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
M. Saniga
中科院分区：
文献类型：
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作者：
H. Havlicek;M. Saniga
作为我们先前工作的延续（Havlicek and Saniga 2007 J. Phys.）。答:数学。（gen 40 F943-52）（预印本0708.4333）)对单个d维qubit进行了代数几何研究，其中d是任意正整数。本文的研究是基于qudit的广义泡利群的辛模与（模）环上投影线的精细结构之间的复杂关系。给出了与给定泡利算子交换的广义泡利算子的个数和包含相应向量的投影线上的点的个数的显式公式。值得注意的是，除非d是不同素数的乘积，否则补集不是相关投影线上对应点的集合论并。根据它们表示向量的程度，这些算子也被构造成不相交的“层”。并与一些多量程案例作了简要比较。
As a continuation of our previous work (Havlicek and Saniga 2007 J. Phys. A: Math. Gen. 40 F943–52 (Preprint 0708.4333)) an algebraic geometrical study of a single d-dimensional qudit is made, with d being any positive integer. The study is based on an intricate relation between the symplectic module of the generalized Pauli group of the qudit and the fine structure of the projective line over the (modular) ring . Explicit formulae are given for both the number of generalized Pauli operators commuting with a given one and the number of points of the projective line containing the corresponding vector of . We find, remarkably, that a perp-set is not a set-theoretic union of the corresponding points of the associated projective line unless d is a product of distinct primes. The operators are also seen to be structured into disjoint ‘layers’ according to the degree of their representing vectors. A brief comparison with some multiple-qudit cases is made.