论文标题
沃纳国家的扩展性
Extendibility of Werner States
论文作者
论文摘要
我们研究了Werner状态的双面对称扩展性问题。这些状态的统一对称性的相互作用以及扩展性场景的固有的两部分置换对称性使我们能够将此问题映射到高度对称的自旋模型哈密顿量的基态问题中。我们通过利用SU（D）的表示理论来分析基础状态问题，尤其是与Littlewood-Richarson分解中年轻图的优势顺序有关的结果。结果，我们为Werner State的扩展性提供了必要和充分的条件，以进行任意扩展大小和局部尺寸。有趣的是，延伸状态的范围在两侧的扩展大小之间存在非平凡的权衡。我们将我们的结果与各向同性状态的双面扩展性问题进行了比较，那里没有这种权衡。
We investigate the two-sided symmetric extendibility problem of Werner states. The interplay of the unitary symmetry of these states and the inherent bipartite permutation symmetry of the extendibility scenario allows us to map this problem into the ground state problem of a highly symmetric spin-model Hamiltonian. We solve this ground state problem analytically by utilizing the representation theory of SU(d), in particular a result related to the dominance order of Young diagrams in Littlewood-Richarson decompositions. As a result, we obtain necessary and sufficient conditions for the extendibility of Werner states for arbitrary extension size and local dimension. Interestingly, the range of extendible states has a non-trivial trade-off between the extension sizes on the two sides. We compare our result with the two-sided extendibility problem of isotropic states, where there is no such trade-off.
