Tumula信息与双重最小化Petz Renyi lautum信息
Tumula information and doubly minimized Petz Renyi lautum information
AI总结：
本文研究了lautum信息的双重最小化变体，提出tumula信息及其Petz Renyi版本，探讨了其性质和在假设检验中的应用。
摘要：
我们研究了一种lautum信息的双重最小化变体——一种互信息的反向类比，定义为任何产品态与固定双分量子态之间的最小相对熵；我们称此度量为tumula信息。此外，我们引入了相应的Petz Renyi版本，称为双重最小化Petz Renyi lautum信息（PRLI）。我们推导了这些相关度量的几个一般性质，并在假设检验的背景下提供了操作解释。具体而言，我们展示了某些二元量子态鉴别问题的反向直接指数由双重最小化PRLI的阶数α∈(0,1/2)量化，且Sanov指数由tumula信息确定。此外，我们探讨了tumula信息扩展到通道的应用，并将其性质与先前关于通道umlaut信息的研究进行了比较。
英文摘要：
We study a doubly minimized variant of the lautum information - a reversed analogue of the mutual information - defined as the minimum relative entropy between any product state and a fixed bipartite quantum state; we refer to this measure as the tumula information. In addition, we introduce the corresponding Petz Renyi version, which we call the doubly minimized Petz Renyi lautum information (PRLI). We derive several general properties of these correlation measures and provide an operational interpretation in the context of hypothesis testing. Specifically, we show that the reverse direct exponent of certain binary quantum state discrimination problems is quantified by the doubly minimized PRLI of order $α\in (0,1/2)$, and that the Sanov exponent is determined by the tumula information. Furthermore, we investigate the extension of the tumula information to channels and compare its properties with previous results on the channel umlaut information [Girardi et al., arXiv:2503.21479].
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