素维Hilbert空间中相干投影的等价类：Q函数及其Gini指标
Equivalence classes of coherent projectors in a Hilbert space with prime dimension: Q functions and their Gini index
摘要：
在Hilbert空间具有奇素数维数$d$的量子系统中，引入了有限个相干态所构成的相干子空间。所有相干子空间的集合被划分为等价类，每个等价类中有$d^2$子空间，等价类中相应的相干投影子具有位移闭包性质，并可分解恒等式.不同的等价类提供了希尔伯特空间的不同粒度化，它们形成了一个偏序“粗”（和“细”）。在由两个相干态张成的二维相干子空间的情况下，对应的投影器（秩为$2$）不同于到与两个相干态中的每一个相关的子空间的两个投影器的和。我们量化这与“非加性运营商”这是一个措施的量子干涉相空间，也是非交换性的投影仪。在给定等价类的相干投影基础上，给出了密度矩阵的广义$Q$和$P$函数.类似的洛伦兹值和基尼指数（这是流行的数量在数学经济学）在这里被用来量化的不平等分布的$Q$功能的量子态，在颗粒结构的希尔伯特空间。.
英文摘要：
Coherent subspaces spanned by a finite number of coherent states are introduced, in a quantum system with Hilbert space that has odd prime dimension $d$. The set of all coherent subspaces is partitioned into equivalence classes, with $d^2$ subspaces in each class.The corresponding coherent projectors within an equivalence class, have the `closure under displacements property' and also resolve the identity. Different equivalence classes provide different granularisation of the Hilbert space, and they form a partial order `coarser' (and `finer'). In the case of a two-dimensional coherent subspace spanned by two coherent states, the corresponding projector (of rank $2$) is different than the sum of the two projectors to the subspaces related to each of the two coherent states. We quantify this with `non-addditivity operators' which are a measure of quantum interference in phase space, and also of the non-commutativity of the projectors. Generalized $Q$ and $P$ functions of density matrices, which are based on coherent projectors in a given equivalence class, are introduced. Analogues of the Lorenz values and the Gini index (which are popular quantities in Mathematical Economics) are used here to quantify the inequality in the distribution of the $Q$ function of a quantum state, within the granular structure of the Hilbert space....
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。
