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arXiv 2008.04362quant-phmath-phmath.MP
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范数函数诱导的相干测度

Coherence measures induced by norm functions

Yangping Jing, Chi-Kwong Li, Edward Poon, Chengyang Zhang

摘要:

哪些矩阵范数能导出量化量子相干性的适当度量?我们研究这个问题的两个重要类的规范,并表明:(i)相干措施不能诱导任何酉相似不变的规范,和(ii)$\ell_{q,p}$ -规范诱导的相干措施,当且仅当$q=1$和$1 \leq p \leq 2$,从而给出了一类新的相干措施,简单的封闭形式,易于计算。这些结果扩展和统一以前已知的事实规范诱导的连贯措施,并导致更广泛的框架,了解什么泛函可以连贯措施。

英文摘要:

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 $\ell_{q,p}$-norm induces a coherence measure if and only if $q=1$ and $1 \leq p \leq 2$, 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.

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。

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