Tumula information and doubly minimized Petz Renyi lautum information

TL;DR

This paper introduces the tumula and doubly minimized Petz Renyi lautum information as new quantum correlation measures, explores their properties, and provides operational interpretations in quantum hypothesis testing and channel analysis.

Contribution

It defines novel quantum correlation measures, derives their properties, and links them to quantum hypothesis testing and channel information, extending previous concepts.

Findings

Doubly minimized PRLI quantifies quantum state discrimination exponents.

Tumula information relates to Sanov exponents in quantum hypothesis testing.

Properties of these measures are compared with existing channel information metrics.

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 $\alpha\in (0,1/2)$, 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].