Inequalities for quantum divergences and the Audenaert–Datta conjecture
Abstract
Given two density matrices ρ and σ, there are a number of different expressions that reduce to the α-Rényi relative entropy of ρ with respect to σ in the classical case; i.e. when ρ and σ commute. Only those expressions for which the data processing inequality (DPI) is valid are of potential interest as quantum divergences in quantum information theory. Audenaert and Datta have made a conjecture on the validity of the DPI for an interesting family of quantum generalizations of the α-Rényi relative entropies, the α - z-Rényi relative entropies. They and others have contributed to the partial solution of this conjecture. We review the problem, its context, and the methods that have been used to obtain the results that are known at present, presenting a unified treatment of developments that have unfolded in a number of different papers.
Additional Information
© 2018 IOP Publishing Ltd. Received 11 June 2018; Accepted 16 October 2018; Accepted Manuscript online 16 October 2018; Published 5 November 2018. US National Science Foundation grants DMS-1363432 (RLF), DMS-1501007 (EAC), PHY-1265118 (EHL) are acknowledged.Attached Files
Submitted - 1806.03985.pdf
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Additional details
- Eprint ID
- 90671
- DOI
- 10.1088/1751-8121/aae8a3
- Resolver ID
- CaltechAUTHORS:20181106-123858044
- DMS-1363432
- NSF
- DMS-1501007
- NSF
- PHY-1265118
- NSF
- Created
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2018-11-06Created from EPrint's datestamp field
- Updated
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2022-07-12Created from EPrint's last_modified field