论文标题
区分性的独立性和系统的维度
The Independence of Distinguishability and the Dimension of the System
论文作者
论文摘要
关于量子状态的区别，尤其是局部区分性的实质性研究。结果表明，局部可区分状态集的必要条件是总施密特等级不大于系统维度。但是，如果我们在较大的系统中查看状态，则限制将是无效的。因此，自然问题是，可以通过在不使用额外资源的情况下在较大的系统中查看它们可以区分难以区分的状态。在本文中，我们认为（完美或明确的）LOCC $ _ {1} $，PPT和SEP SECTISNISSIOMS的此问题。我们证明，如果一组状态在$ \ otime _ {k = 1}^{k} c^{d _ {k}} $中，那么即使在$ \ otimes _ {k = 1}^k}^k} c^c^k} $中也无法分辨，即使在$ \ otimes _ {k = 1} _ {k} \ geqslant2，h _ {k} \ geqslant0 $是整数。这表明这种区别是国家本身的特性，独立于量子系统的维度。我们的结果给出了LOCC $ _ {1} $可区分状态的最大数量，并且可以用来在一般系统中构建LOCC难以区分的产品基础。我们的结果适用于通用系统中的一般状态。为了进行进一步的讨论，我们定义了局部全球不可分割的特性，并提出了一个猜想。
The are substantial studies on distinguishabilities, especially local distinguishability, of quantum states. It is shown that a necessary condition of a local distinguishable state set is the total Schmidt rank not larger than the system dimension. However, if we view states in a larger system, the restriction will be invalid. Hence, a nature problem is that can indistinguishable states become distinguishable by viewing them in a larger system without employing extra resources. In this paper, we consider this problem for (perfect or unambiguous) LOCC$_{1}$, PPT and SEP distinguishabilities. We demonstrate that if a set of states is indistinguishable in $\otimes _{k=1}^{K} C^{d _{k}}$, then it is indistinguishable even being viewed in $\otimes _{k=1}^{K} C^{d _{k}+h _{k}}$, where $K, d _{k}\geqslant2, h _{k}\geqslant0$ are integers. This shows that such distinguishabilities are properties of states themselves and independent of the dimension of quantum system. Our result gives the maximal numbers of LOCC$_{1}$ distinguishable states and can be employed to construct a LOCC indistinguishable product basis in general systems. Our result is suitable for general states in general systems. For further discussions, we define the local-global indistinguishable property and present a conjecture.
