While various coherence measures based on the framework for quantifying coherence [T. Baumgratz, M. Cramer, and M. B. Plenio, Phys. Rev. Lett. 113, 140401 (2014)] have been proposed, it is often asked whether a coherence measure fulfills the maximal value condition that only maximally coherent states should achieve the maximal value of a coherence measure [Y. Peng, Y. Jiang, and H. Fan, Phys. Rev. A 93, 032326 (2016)]. Although it may be easy to rule out the measures that violate the condition by giving a counterexample, it is usually complicated to confirm the validity of the condition for a general coherence measure due to the deal with all mixed states. In this paper, we prove that the maximal value condition of coherence measures holds for mixed states if and only if it holds for a special subset of pure states. Our finding can greatly reduce the examination of whether a coherence measure fulfills the maximal value condition since one only needs to consider a subset of pure states, avoiding the work of considering mixed states.

中文翻译：

---

相干测度的最大值条件在混合状态下成立，并且仅在纯状态下成立

同时基于量化连贯性框架的各种连贯性度量[T。Baumgratz，M.Cramer和MB Plenio，物理学。牧师 [ 113，140401（2014）]已经提出，经常询问相干度量是否满足最大值条件，即只有最大相干状态才应达到相干度量的最大值[Y. 彭Y江和范海 版本A 93032326（2016）]。尽管通过举个反例来排除违反条件的措施可能很容易，但是由于处理了所有混合状态，通常对于确认一般一致性措施的条件的有效性通常很复杂。在本文中，我们证明相干性测度的最大值条件仅在特殊状态的纯态子集成立时才适用于混合态。我们的发现可以极大地减少对相干性度量是否满足最大值条件的检查，因为仅需考虑纯态的子集，而无需考虑混合态。