论文标题
具有主要维度的希尔伯特空间中相干投影仪的等效类别：Q功能及其Gini索引
Equivalence classes of coherent projectors in a Hilbert space with prime dimension: Q functions and their Gini index
论文作者
论文摘要
引入了有限数量的连贯状态的连贯子空间，它的量子系统具有Hilbert Space，其具有奇怪的Prime Dimension $ d $。所有相干子空间的集合都分为等价类别，每个类别都有$ d^2 $子空间。等价类中的相应相干投影仪具有“位移属性下的关闭属性”，也可以解决身份。不同的等效类提供了希尔伯特空间的不同粒度化，它们形成了部分秩序“ coarser”（和``finer''）。在两个连贯状态跨越的二维连贯子空间中，相应的投影仪（等级$ 2 $）与与两个相干态相关的子空间的两个投影仪的总和不同。我们用“非辅助操作员”对此进行了量化，这是对相空间中量子干扰以及投影仪的非交通性的量度。介绍了基于给定等价类中的连贯投影仪的通用$ q $和$ p $函数。 Lorenz值和Gini指数的类似物（在数学经济学中是流行的数量）用于量化Hilbert Space的粒状结构内的量子状态$ Q $函数的分布的不平等...。
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....
