局域态鉴别问题中的纠缠电池与纠缠催化剂
Entanglement battery and entanglement catalyst in local state discrimination problems
AI总结：
该研究探讨局域态鉴别中纠缠电池与纠缠催化剂的优劣，明确精确情形下完美鉴别正交双体纠缠纯态的条件，构造实例证明其优势，发现近似工具在特定局域态鉴别中作用显著。
AI中文摘要：
本工作研究在局域态鉴别问题中使用纠缠电池（entanglement battery）和纠缠催化剂（entanglement catalyst）的局限性与优势，考虑这两种工具的精确情形与近似情形。我们证明，在局域操作和经典通信（LOCC）下，要使用精确纠缠电池或精确纠缠催化剂完美鉴别任意一组正交双体纠缠纯态，该集合的基数必须小于给定希尔伯特空间的总维数。随后，我们构造了一个非平凡情形，其中精确纠缠电池可提供巨大优势；还构造了其他非平凡情形，其中精确或近似纠缠电池、纠缠催化剂均有用。实际上，我们发现近似工具在鉴别某些可由多份拷贝不可区分系综导出的集合的局域态时特别有用。
英文摘要：
In this work, we study the limitations and advantages of using entanglement battery and entanglement catalyst in local state discrimination problems. We consider both cases of such tools, i.e., exact and approximate cases. We show that to distinguish any set of orthogonal pure bipartite entangled states perfectly under local operations and classical communication using an (exact) entanglement battery or an (exact) entanglement catalyst, it is necessary to consider that the cardinality of the set must be smaller than the total dimension of the given Hilbert space. Then, we construct a nontrivial case where an exact entanglement battery can provide huge advantage. We also construct other nontrivial cases where exact or approximate entanglement battery or entanglement catalyst can be useful. In fact, we find that the approximate tools are particularly useful in the local discrimination of certain sets which can be derived from many-copy indistinguishable ensembles.
