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 ...

中文翻译：

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希尔伯特空间中具有素数维的相干投影仪的等价类：Q函数及其基尼系数

在具有希尔伯特空间且奇数维数为d的量子系统中，引入了由有限数量的相干态跨越的相干子空间。所有相干子空间的集合被划分为等价类，每个类中有d 2个子空间。等效类内的相应相干投影机具有“位移关闭属性”，并且还可以解析身份。不同的等价类提供了希尔伯特空间的不同粒度，并且它们形成了部分顺序的“粗化器”（和“细化器”）。在二维相干子空间跨越两个相干状态的情况下，对应的投影仪（等级2）不同于两个投影仪与与两个相干状态中的每一个相关的子空间的总和。我们用“非可加性算子”对此进行量化，该算子可测量相空间中的量子干扰以及投影仪的非可交换性。广义Q和...