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Quantum Markov chains and logarithmic trace inequalities

Sutter, David and Berta, Mario and Tomamichel, Marco (2017) Quantum Markov chains and logarithmic trace inequalities. In: 2017 IEEE International Symposium on Information Theory (ISIT). IEEE , Piscataway, NJ, pp. 1988-1992. ISBN 978-1-5090-4096-4.

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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.

Item Type:Book Section
Related URLs:
URLURL TypeDescription
Berta, Mario0000-0002-0428-3429
Tomamichel, Marco0000-0001-5410-3329
Additional Information:© 2017 IEEE. DS acknowledges support by the Swiss National Science Foundation (SNSF) via the National Centre of Competence in Research “QSIT” and by the European Commission via the project “RAQUEL”. MB acknowledges funding by the SNSF through a fellowship, funding by the Institute for Quantum Information and Matter (IQIM), an NSF Physics Frontiers Center (NFS Grant PHY-1125565) with support of the Gordon and Betty Moore Foundation (GBMF-12500028), and funding support form the ARO grant for Research on Quantum Algorithms at the IQIM (W911NF-12-1-0521). MT is funded by an ARC Discovery Early Career Researcher Award (DECRA) fellowship and acknowledges support from the ARC Centre of Excellence for Engineered Quantum Systems (EQUS).
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Swiss National Science Foundation (SNSF)UNSPECIFIED
European CommissionUNSPECIFIED
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Gordon and Betty Moore FoundationGBMF-12500028
Army Research Office (ARO)W911NF-12-1-0521
Australian Research CouncilUNSPECIFIED
Record Number:CaltechAUTHORS:20170816-174117187
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Official Citation:D. Sutter, M. Berta and M. Tomamichel, "Quantum Markov chains and logarithmic trace inequalities," 2017 IEEE International Symposium on Information Theory (ISIT), Aachen, Germany, 2017, pp. 1988-1992. doi: 10.1109/ISIT.2017.8006877
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:80541
Deposited On:17 Aug 2017 20:15
Last Modified:15 Nov 2021 19:36

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