Space-time generalization of mutual information
- URL: http://arxiv.org/abs/2401.02475v1
- Date: Thu, 4 Jan 2024 19:00:00 GMT
- Title: Space-time generalization of mutual information
- Authors: Paolo Glorioso, Xiao-Liang Qi, Zhenbin Yang
- Abstract summary: We introduce a space-time generalization of mutual information which satisfies several natural properties of the mutual information.
In particular, this quantity, that we call the emphspace-time mutual information, bounds all dynamical correlations.
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.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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 the
\emph{space-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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