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Relative entropy for von Neumann subalgebras
International Journal of Mathematics ( IF 0.6 ) Pub Date : 2020-03-07 , DOI: 10.1142/s0129167x20500469
Li Gao 1 , Marius Junge 2 , Nicholas LaRacuente 3
Affiliation  

We revisit the connection between index and relative entropy for an inclusion of finite von Neumann algebras. We observe that the Pimsner–Popa index connects to sandwiched [Formula: see text]-Rényi relative entropy for all [Formula: see text], including Umegaki’s relative entropy at [Formula: see text]. Based on that, we introduce a new notation of relative entropy to a subalgebra which generalizes subfactors index. This relative entropy has application in estimating decoherence time of quantum Markov semigroups.

中文翻译:

冯诺依曼子代数的相对熵

我们重新审视指数和相对熵之间的联系,以包含有限冯诺依曼代数。我们观察到 Pimsner-Popa 指数连接到夹层的 [公式:见文本]-Rényi 相对熵为所有 [公式:见文本],包括 Umegaki 在 [公式:见文本] 处的相对熵。在此基础上,我们将一种新的相对熵表示法引入到泛化子因子索引的子代数中。这种相对熵可用于估计量子马尔可夫半群的退相干时间。
更新日期:2020-03-07
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