Tumula information and doubly minimized Petz Renyi lautum information

Quantum Physics [Submitted on 17 Mar 2026] Tumula information and doubly minimized Petz Renyi lautum information Lukas Schmitt, Filippo Girardi, Laura Burri 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 \alpha\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]. Comments: 18+19 pages, 2 figures, 3 tables Subjects: Quantum Physics (quant-ph); Information Theory (cs.IT) Cite as: arXiv:2603.17005 [quant-ph]   (or arXiv:2603.17005v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.17005 Focus to learn more Submission history From: Laura Burri [view email] [v1] Tue, 17 Mar 2026 18:00:05 UTC (235 KB) Access Paper: view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 Change to browse by: cs cs.IT math math.IT References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)