Tumula information and doubly minimized Petz Renyi lautum information

2026-03-17

AI Summary

This work investigates an optimized formulation of lautum information within quantum correlation measures and its operational significance in quantum hypothesis testing. It introduces a novel doubly minimized variant—termed tumula information—and its Petz–Rényi counterpart, defined via minimization of the quantum relative entropy between product states and a given bipartite state. For the first time, the study establishes an exact connection between this measure and the reverse direct exponent (for α ∈ (0, 1/2)) as well as the Sanov exponent in quantum state discrimination, extending these results to the setting of quantum channels. By integrating quantum relative entropy, Petz–Rényi divergences, and variational optimization techniques, the paper systematically derives fundamental properties of the proposed quantities and elucidates their role in quantifying distinguishability for both bipartite quantum states and quantum channels.

Technology Category

• Machine Learning: Information Theory
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Search and Optimization: Distributed Search

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Web Mining and Content Analysis: Content-based information diffusion

Abstract

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].

Problem

• lautum information
• quantum correlation
• hypothesis testing
• Rényi divergence
• quantum channels

Innovation

• tumula information
• Petz-Rényi lautum information
• quantum hypothesis testing
• Sanov exponent
• quantum correlations