Tumula information and doubly minimized Petz Renyi lautum information
This work addresses theoretical challenges in quantum information theory by providing new correlation measures with operational interpretations, though it appears incremental as it builds on existing concepts like lautum information.
The paper tackles the problem of quantifying correlations in quantum systems by introducing a doubly minimized variant of lautum information, called tumula information, and its Petz Renyi version, showing that these measures determine exponents in binary quantum state discrimination and Sanov exponent problems.
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].