Optimized Quantum F-Divergences
Optimized Quantum F-Divergences
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DOI：
10.1109/isit.2018.8437925
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发表时间：
2018-06
期刊：
影响因子：
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通讯作者：
M. Wilde
中科院分区：
文献类型：
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作者：
M. Wilde
量子相对熵是两个量子态可分离性的度量，是量子信息论中的一个统一概念：许多信息度量，如熵、条件熵、互信息和纠缠度量都可以由它实现，因此，人们对推广这个概念以进一步理解它的最基本性质有着广泛的兴趣，其中之一就是数据处理不等式。Petz的量子f-发散是量子相对熵的一种推广，它也导致了其他相对熵，如Petz-Renyi相对熵。在这篇文章中，我介绍了优化的量子$f$发散量子相对熵的相关推广。我证明了它满足数据处理不等式，证明的方法依赖于运营商詹森不等式，类似于Petz的原始方法。有趣的是，三明治Renyi相对熵是优化的$f$-发散的特殊例子。因此，这种方法的一个好处是，现在有一个单一的，统一的方法来建立的Petz-Renyi和三明治Renyi相对熵的数据处理不等式，为它是已知的持有的参数的全部范围。本文的完整版本可在arXiv：1710.10252上访问
The quantum relative entropy is a measure of the distinguishability of two quantum states, and it is a unifying concept in quantum information theory: many information measures such as entropy, conditional entropy, mutual information, and entanglement measures can be realized from it. As such, there has been broad interest in generalizing the notion to further understand its most basic properties, one of which is the data processing inequality. The quantum $f$-divergence of Petz is one generalization of the quantum relative entropy, and it also leads to other relative entropies, such as the Petz-Renyi relative entropies. In this contribution, I introduce the optimized quantum $f$-divergence as a related generalization of quantum relative entropy. I prove that it satisfies the data processing inequality, and the method of proof relies upon the operator Jensen inequality, similar to Petz's original approach. Interestingly, the sandwiched Renyi relative entropies are particular examples of the optimized $f$-divergence. Thus, one benefit of this approach is that there is now a single, unified approach for establishing the data processing inequality for both the Petz-Renyi and sandwiched Renyi relative entropies, for the full range of parameters for which it is known to hold. Full version of this paper is accessible at arXiv:1710.10252