论文标题
关于从无法扩展的产品基础构建真正纠缠的子空间的负面结果
Negative result about the construction of genuinely entangled subspaces from unextendible product bases
论文作者
论文摘要
不可扩展的产品库（UPB）提供了一种多功能工具，这些工具在量子信息理论的不同领域跨越了各种应用。因此，它们的全面特征非常重要，并且在二十年中一直是重要的兴趣主题。一个公开的问题询问了UPB的存在，UPB的存在，这些UPB确实是不可避免的，即，即使使用双重载体，它们也无法扩展。换句话说，问题是要验证是否存在真正纠缠的子空间（GESS），该子空间仅由真正的多方纠缠状态组成，对UPBS互补。在不同的多部分方案中，我们将许多尺寸的UPBs解决了这个问题。特别是，在最大的局部维度的最重要情况下，我们表明，这种UPB总是有禁忌的基础性，包括与最大维度相对应的最小值。
Unextendible product bases (UPBs) provide a versatile tool with various applications across different areas of quantum information theory. Their comprehensive characterization is thus of great importance and has been a subject of vital interest for over two decades now. An open question asks about the existence of UPBs, which are genuinely unextendible, i.e., they are not extendible even with biproduct vectors. In other words, the problem is to verify whether there exist genuinely entangled subspaces (GESs), subspaces composed solely of genuinely multiparty entangled states, complementary to UPBs. We solve this problem in the negative for many sizes of UPBs in different multipartite scenarios. In particular, in the all-important case of equal local dimensions, we show that there are always forbidden cardinalities for such UPBs, including the minimal ones corresponding to GESs of the maximal dimensions.
