Quantum Markov chains and logarithmic trace inequalities

Sutter, D; Berta, M; Tomamichel, M

Quantum Markov chains and logarithmic trace inequalities

Sutter, D Berta, M Tomamichel, M

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Publication Type:: Conference Proceeding
Citation:: IEEE International Symposium on Information Theory - Proceedings, 2017, pp. 1988 - 1992
Issue Date:: 2017-08-09

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Field	Value	Language
dc.contributor.author	Sutter, D	en_US
dc.contributor.author	Berta, M	en_US
dc.contributor.author	Tomamichel, M https://orcid.org/0000-0001-5410-3329	en_US
dc.date.issued	2017-08-09	en_US
dc.identifier.citation	IEEE International Symposium on Information Theory - Proceedings, 2017, pp. 1988 - 1992	en_US
dc.identifier.isbn	9781509040964	en_US
dc.identifier.issn	2157-8095	en_US
dc.identifier.uri	http://hdl.handle.net/10453/126051
dc.description.abstract	© 2017 IEEE. A Markov chain is a tripartite quantum state ρABC where there exists a recovery map RB→BC such that ρABC = RB→BC(ρAB). More generally, an approximate Markov chain ρABC is a state whose distance to the closest recovered state RB→BC(ρAB) is small. Recently it has been shown that this distance can be bounded from above by the conditional mutual information I(A: C\|B)ρ of the state. We improve on this connection by deriving the first bound that is tight in the commutative case and features an explicit recovery map that only depends on the reduced state pBC. The key tool in our proof is a multivariate extension of the Golden-Thompson inequality, which allows us to extend logarithmic trace inequalities from two to arbitrarily many matrices.	en_US
dc.relation	http://purl.org/au-research/grants/arc/DE160100821
dc.relation.ispartof	IEEE International Symposium on Information Theory - Proceedings	en_US
dc.relation.isbasedon	10.1109/ISIT.2017.8006877	en_US
dc.title	Quantum Markov chains and logarithmic trace inequalities	en_US
dc.type	Conference Proceeding
utslib.for	0802 Computation Theory and Mathematics	en_US
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	closed_access
pubs.publication-status	Published	en_US

Abstract:

© 2017 IEEE. A Markov chain is a tripartite quantum state ρABC where there exists a recovery map RB→BC such that ρABC = RB→BC(ρAB). More generally, an approximate Markov chain ρABC is a state whose distance to the closest recovered state RB→BC(ρAB) is small. Recently it has been shown that this distance can be bounded from above by the conditional mutual information I(A: C|B)ρ of the state. We improve on this connection by deriving the first bound that is tight in the commutative case and features an explicit recovery map that only depends on the reduced state pBC. The key tool in our proof is a multivariate extension of the Golden-Thompson inequality, which allows us to extend logarithmic trace inequalities from two to arbitrarily many matrices.

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http://hdl.handle.net/10453/126051