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A<sc>bstract</sc> We explore a large class of correlation measures called theα−zRényi mutual informations (RMIs). Unlike the commonly used notion of RMI involving linear combinations of Rényi entropies, theα−zRMIs are positive semi-definite and monotonically decreasing under local quantum operations, making them sensible measures of total (quantum and classical) correlations. This follows from their descendance from Rényi relative entropies. In addition to upper bounding connected correlation functions between subsystems, we prove the much stronger statement that for certain values ofαandz, theα−zRMIs also lower bound certain connected correlation functions. We develop an easily implementable replica trick which enables us to compute theα−zRMIs in a variety of many-body systems including conformal field theories, free fermions, random tensor networks, and holography.
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Space-time generalization of mutual information
A<sc>bstract</sc> The mutual information characterizes correlations between spatially separated regions of a system. Yet, in experiments we often measure dynamical correlations, which involve probing operators that are also separated in time. Here, we introduce a space-time generalization of mutual information which, by construction, satisfies several natural properties of the mutual information and at the same time characterizes correlations across subsystems that are separated in time. In particular, this quantity, that we call thespace-time mutual information, bounds all dynamical correlations. We construct this quantity based on the idea of the quantum hypothesis testing. As a by-product, our definition provides a transparent interpretation in terms of an experimentally accessible setup. We draw connections with other notions in quantum information theory, such as quantum channel discrimination. Finally, we study the behavior of the space-time mutual information in several settings and contrast its long-time behavior in many-body localizing and thermalizing systems.
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- Award ID(s):
- 2111998
- PAR ID:
- 10557737
- Publisher / Repository:
- Journal of High Energy Physics
- Date Published:
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2024
- Issue:
- 5
- ISSN:
- 1029-8479
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/JHEP05(2024)338
