Rényi generalizations of the conditional quantum mutual information
The conditional quantum mutual information I(A; BC) of a tripartite state ρ{sub ABC} is an information quantity which lies at the center of many problems in quantum information theory. Three of its main properties are that it is nonnegative for any tripartite state, that it decreases under local operations applied to systems A and B, and that it obeys the duality relation I(A; BC) = I(A; BD) for a fourparty pure state on systems ABCD. The conditional mutual information also underlies the squashed entanglement, an entanglement measure that satisfies all of the axioms desired for an entanglement measure. As such, it has been an open question to find Rényi generalizations of the conditional mutual information, that would allow for a deeper understanding of the original quantity and find applications beyond the traditional memoryless setting of quantum information theory. The present paper addresses this question, by defining different αRényi generalizations I{sub α}(A; BC) of the conditional mutual information, some of which we can prove converge to the conditional mutual information in the limit α → 1. Furthermore, we prove that many of these generalizations satisfy nonnegativity, duality, and monotonicity with respect to local operations on one of the systems A ormore »
 Authors:

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 Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125 (United States)
 Department of Physics and Astronomy, Hearne Institute for Theoretical Physics, Louisiana State University, Baton Rouge, Louisiana 70803 (United States)
 (United States)
 Publication Date:
 OSTI Identifier:
 22403104
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 2; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; INFORMATION THEORY; PURE STATES; QUANTUM ENTANGLEMENT; QUANTUM INFORMATION