Decomposition Rules for Quantum Rényi Mutual Information with an Application to Information Exclusion Relations

McKinlay, A; Tomamichel, M

Decomposition Rules for Quantum Rényi Mutual Information with an Application to Information Exclusion Relations

McKinlay, A Tomamichel, M

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Field	Value	Language
dc.contributor.author	McKinlay, A	en_US
dc.contributor.author	Tomamichel, M https://orcid.org/0000-0001-5410-3329	en_US
dc.identifier.uri	http://hdl.handle.net/10453/138680
dc.description.abstract	We prove decomposition rules for quantum R\'enyi mutual information, generalising the relation $I(A:B) = H(A) - H(A\|B)$ to inequalities between R\'enyi mutual information and R\'enyi entropy of different orders. The proof uses Beigi's generalisation of Reisz-Thorin interpolation to operator norms, and a variation of the argument employed by Dupuis which was used to show chain rules for conditional R\'enyi entropies. The resulting decomposition rule is then applied to establish an information exclusion relation for R\'enyi mutual information, generalising the original relation by Hall.	en_US
dc.rights	info:eu-repo/semantics/openAccess
dc.title	Decomposition Rules for Quantum Rényi Mutual Information with an Application to Information Exclusion Relations	en_US
dc.type	Journal Article
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Computer Science
pubs.organisational-group	/University of Technology Sydney/Strength - QSI - Centre for Quantum Software and Information
utslib.copyright.status	open_access	*

Abstract:

We prove decomposition rules for quantum R\'enyi mutual information, generalising the relation $I(A:B) = H(A) - H(A|B)$ to inequalities between R\'enyi mutual information and R\'enyi entropy of different orders. The proof uses Beigi's generalisation of Reisz-Thorin interpolation to operator norms, and a variation of the argument employed by Dupuis which was used to show chain rules for conditional R\'enyi entropies. The resulting decomposition rule is then applied to establish an information exclusion relation for R\'enyi mutual information, generalising the original relation by Hall.

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http://hdl.handle.net/10453/138680