Quantum data processing inequality bounds the set of bipartite states that can be generated by two far apart parties under local operations; Having access to a bipartite state as a resource, two parties cannot locally transform it to another bipartite state with a mutual information greater than that of the resource state. But due to the additivity of quantum mutual information under tensor product, the data processing inequality gives no bound when the parties are provided with arbitrary number of copies of the resource state. In this paper we introduce a measure of correlation on bipartite quantum states, called maximal correlation, that is not additive and gives the same number when computed for multiple copies. Then by proving a data processing inequality for this measure, we find a bound on the set of states that can be generated under local operations even when an arbitrary number of copies of the resource state is available.

翻译：量子数据处理不等式限制了在局域操作下两个相距遥远的参与者所能产生的二分量子态集合；当拥有一个二分量子态作为资源时，双方无法通过局域操作将其转化为另一个互信息大于资源态互信息的二分量子态。但由于量子互信息在张量积下具有可加性，当参与者获得任意多个资源态的副本时，数据处理不等式不再提供任何限制。本文引入了一种关于二分量子态关联性的度量，称为最大关联性，该度量不可加，且在对多个副本进行计算时给出相同数值。通过证明该度量的数据处理不等式，我们找到了在即使拥有任意多个资源态副本的情况下，局域操作所能产生的量子态集合的一个界限。