Which matrix norms induce proper measures for quantifying quantum coherence? We study this problem for two important classes of norms and show that (i) coherence measures cannot be induced by any unitary similarity invariant norm and (ii) the ℓ_q,p-norm induces a coherence measure if and only if q = 1 and 1 ≤ p ≤ 2, thus giving a new class of coherence measures with simple closed forms that are easy to compute. These results extend and unify previously known facts about norm-induced coherence measures and lead to a broader framework for understanding what functionals can be coherence measures.

中文翻译：

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规范函数引起的连贯性度量

哪些矩阵规范引发了量化量子相干性的适当措施？我们为规范的两个重要的类研究这个问题，并显示其（i）相干性措施不能由任何单一的相似性不变范数和（ii）的感应ℓ _q，p范数诱导相干性测量当且仅当q = 1和1个≤ p ≤2，由此得到一类新的相干性措施，很容易计算简单的封闭形式。这些结果扩展并统一了有关规范引发的一致性度量的先前已知事实，并导致了一个更广泛的框架来理解什么功能可以作为一致性度量。