689 research outputs found
A Singular Value Inequality for Heinz Means
We prove a matrix inequality for matrix monotone functions, and apply it to
prove a singular value inequality for Heinz means recently conjectured by X.
Zhan.Comment: 4 pages; Mistake in proof of Theorem 1 correcte
Trace inequalities for completely monotone functions and Bernstein functions
We prove a matrix trace inequality for completely monotone functions and for
Bernstein functions. As special cases we obtain non-trivial trace inequalities
for the power function x->x^q, which for certain values of q complement
McCarthy's trace inequality and for others strenghten it.Comment: 16 page
Spectral radius of Hadamard product versus conventional product for non-negative matrices
We prove an inequality for the spectral radius of products of non-negative
matrices conjectured by X. Zhan. We show that for all non-negative
matrices and , , where represents the Hadamard product.Comment: 4.1 page
On the asymmetry of the relative entropy
The quantum relative entropy is a widely used dissimilarity
measure between quantum states, but it has the peculiarity of being asymmetric
in its arguments. We quantify the amount of asymmetry by providing a sharp
upper bound in terms of two parameters: the trace norm distance between the two
states, and the smallest of the smallest eigenvalues of both states. The bound
is essentially the asymmetry between two binary distributions governed by these
two parameters.Comment: 9 pages, 3 figure
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