集体完全刻画催化优超关系的不等式
Inequalities that Collectively Completely Characterize the Catalytic Majorization Relation
摘要：
对于概率向量x和y，催化优化关系x prec_T y被定义为当存在概率向量z使得x otimes z被y otimes z优化时成立。本文给出了一个无限函数族，使得在某些平凡的限制下，x prec_T_y当且仅当对族中所有函数f_r，f_r（x）< f_r（y）.提供了一个证明这一结果的大纲。已知催化优化关系提供了当可以指定附加的联合保持状态以促进变换而不被消耗时，使用局部操作和经典通信来确定联合保持纯量子态的哪些变换是可能的。
英文摘要：
For probability vectors x and y, the catalytic majorization relation x prec_T y is defined to hold when there exists a probability vector z such that x otimes z is majorized by y otimes z. In this paper, an infinite family of functions is given such that, subject to some trivial restrictions, x prec_T y if and only if f_r(x) < f_r(y) for all functions f_r in the family. An outline of a proof of this result is provided. The catalytic majorization relation is known to provide a determination of which transformations of jointly held pure quantum states are possible using local operations and classical communication when an additional jointly held state may be specified to facilitate the transformation without being consumed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
