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R'enyi squashed entanglement, discord, and relative entropy differences | | Kaushik P. Seshadreesan
; Mario Berta
; Mark M. Wilde
; | | Date: |
6 Oct 2014 | | Abstract: | In a previous work arXiv:1403.6102, we recently proposed R’enyi
generalizations of the conditional quantum mutual information, which were shown
to satisfy some properties that hold for the original quantity, such as
non-negativity, duality, and monotonicity under local operations on the system
$B$ (with it being left open to show that the R’enyi quantity is monotone
under local operations on system $A$). We also defined a R’enyi squashed
entanglement and a R’enyi quantum discord based upon a R’enyi conditional
quantum mutual information. Here, we investigate these quantities in more
detail. Taking as a conjecture that the R’enyi conditional quantum mutual
information is monotone under local operations on both systems $A$ and $B$, we
prove that the R’enyi squashed entanglement and the R’enyi quantum discord
defined in our prior work satisfy many of the properties of the respective
original von Neumann entropy-based quantities. In arXiv:1403.6102, we also
detailed a procedure to obtain R’enyi generalizations of any quantum
information measure that is equal to a linear combination of von Neumann
entropies with coefficients chosen from the set ${-1,0,1}$. Here, we extend
this procedure to include differences of relative entropies. Using the extended
procedure and a conjectured monotonicity of the R’enyi generalizations in the
R’enyi parameter, we discuss potential remainder terms for well known
inequalities such as monotonicity of the relative entropy, joint convexity of
the relative entropy, and the Holevo bound. | | Source: | arXiv, 1410.1443 | | Services: | Forum | Review | PDF | Favorites | |
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