多体CAT态LOCC不可比较系综的超图理论特征
Hypergraph-theoretic charaterizations for LOCC incomparable ensembles of multipartite CAT states
摘要：
使用图和超图系统地模拟集合的任意子集的缔约方代表{\it合奏（或集合）}的共享的多部CAT状态，我们研究这种{\it合奏}下{\it本地操作和经典通信（LOCC）}之间的转换。我们表明，使用部分熵的标准，任何两个这样的不同的合奏表示{\it $r$-均匀超图}具有相同数量的超边（CAT状态），是LOCC无法比拟的偶数整数$r\geq 2$，推广结果在\cite{mscthesis,sin:pal:kum:sri}。我们证明了由$r$-均匀超图所表示的最大的一组相互LOCC不可比较的集合的基数，即使是$r\geq 2$，是指数的当事人的数量。我们还证明了LOCC之间的不可比性表示的两个合奏的3-均匀超图的部分熵的标准并没有帮助建立不可比性。此外，我们刻画了EPR图的LOCC相似性的模型，LOCC限制到隐形传态和边缘破坏。我们表明，这个模型是等价的，其中LOCC变换进行了一系列的操作，其中每个操作最多增加一个新的EPR对。
英文摘要：
Using graphs and hypergraphs to systematically model collections of arbitrary subsets of parties representing {\it ensembles (or collections)} of shared multipartite CAT states, we study transformations between such {\it ensembles} under {\it local operations and classical communication (LOCC)}. We show using partial entropic criteria, that any two such distinct ensembles represented by {\it $r$-uniform hypergraphs} with the same number of hyperedges (CAT states), are LOCC incomparable for even integers $r\geq 2$, generalizing results in \cite{mscthesis,sin:pal:kum:sri}. We show that the cardinality of the largest set of mutually LOCC incomparable ensembles represented by $r$-uniform hypergraphs for even $r\geq 2$, is exponential in the number of parties. We also demonstrate LOCC incomparability between two ensembles represented by 3-uniform hypergraphs where partial entropic criteria do not help in establishing incomparability. Further we characterize LOCC comparability of EPR graphs in a model where LOCC is restricted to teleportation and edge destruction. We show that this model is equivalent to one in which LOCC transformations are carried out through a sequence of operations where each operation adds at most one new EPR pair.
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