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"mutual information" is a correct and usable phrase in written English.
You can use it when discussing information that is shared between two or more parties. For example, "We exchanged mutual information about our respective interests in the project."
Dictionary
mutual information
noun
A measure of the entropic (informational) correlation between two random variables.
Exact(56)
Figure 6: Mutual information contours.
Kraskov, A., Stögbauer, H. & Grassberger, P. Estimating mutual information.
Mutual Information (MI).
Mutual information registration.
is normalized mutual information.
Deformable registration (with mutual information).
mutual information effective SINR mapping.
Manual registration (with mutual information).
Pointwise mutual information (m i).
Similar(2)
Insist on mutual information-gathering within an erotic context.
mutual information-based discriminant analysis.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com