论文标题
难以理解的产品基库，绑定的纠缠状态和范围标准
Unextendible product bases, bound entangled states, and the range criterion
论文作者
论文摘要
不可扩展的产品基础（UPB）是一组正交产品状态，跨越给定的希尔伯特空间的子空间，而互补子空间不包含产品状态。这些产品库对于产生结合的纠缠（BE）很有用。在这项工作中，我们认为最大尺寸的可降低和不可还原UPB，这可以产生最低等级的状态。从可简化的UPB中，可以在本地消除一个或多个状态，以保持测量后状态正交。另一方面，对于不可还原的UPB，以上是不可能的。特别是，当前尺寸的UPB很重要，因为它们可能有助于生产状态，其等级的品种最宽，可以满足范围标准。在这里，我们谈论这样的国家。我们还提供其他类型的状态并分析各州的某些特性。目前的一些状态与瓷砖结构有关。此外，我们提供了与当前的最低等级状态相对应的不同UPB，并讨论了UPB的重要属性。
An unextendible product basis (UPB) is a set of orthogonal product states which span a subspace of a given Hilbert space while the complementary subspace contains no product state. These product bases are useful to produce bound entangled (BE) states. In this work we consider reducible and irreducible UPBs of maximum size, which can produce BE states of minimum rank. From a reducible UPB, it is possible to eliminate one or more states locally, keeping the post-measurement states orthogonal. On the other hand, for an irreducible UPB, the above is not possible. Particularly, the UPBs of the present size are important as they might be useful to produce BE states, having ranks of the widest variety, which satisfy the range criterion. Here we talk about such BE states. We also provide other types of BE states and analyze certain properties of the states. Some of the present BE states are associated with the tile structures. Furthermore, we provide different UPBs corresponding to the present BE states of minimum rank and discuss important properties of the UPBs.
