Related papers: Generalizations of Powers--Størmer's inequality

Generalizations of Powers--Størmer's inequality

URL: http://arxiv.org/abs/2302.07818v3
Date: Sun, 17 Mar 2024 00:31:23 GMT
Title: Generalizations of Powers--Størmer's inequality
Authors: Mohsen Kian, Mohammad Sal Moslehian, Hiroyuki Osaka,
Abstract summary: mathrmtr|A-B|leq 2, mathrmtrbig(f(A)g(B)big) endalign* holds for every positive-valued matrix monotone function $f$. This study demonstrates that the set of functions satisfying this inequality includes additional elements and provides illustrative examples to support this claim.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: Relating to finding possible upper bounds for the probability of error for discriminating between two quantum states, it is well-known that \begin{align*} \mathrm{tr}(A+B) - \mathrm{tr}|A-B|\leq 2\, \mathrm{tr}\big(f(A)g(B)\big) \end{align*} holds for every positive-valued matrix monotone function $f$, where $g(x)=x/f(x)$, and all positive definite matrices $A$ and $B$. This study demonstrates that the set of functions satisfying this inequality includes additional elements and provides illustrative examples to support this claim. Furthermore, we present a characterization of matrix decreasing functions based on a matrix version of the above inequality.

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