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Quantum Simulation
Some convexity and monotonicity results of trace functionals
arXiv
Authors: Haonan Zhang
Year
2021
Paper ID
62424
Status
Preprint
Abstract Read
~2 min
Abstract Words
117
Citations
N/A
Abstract
In this paper, we prove the convexity of trace functionals $(A,B,C)mapsto Tr|BpACq|s,for parameters(p,q,s)that are best possible, whereBandCare anyn-by-npositive definite matrices, andAis anyn-by-n$ matrix. We also obtain the monotonicity versions of trace functionals of this type. As applications, we extend some results in \cite{HP12quasi,CFL16some} and resolve a conjecture in \cite{RZ14} in the matrix setting. Other conjectures in \cite{RZ14} will also be discussed. We also show that some related trace functionals are not concave in general. Such concavity results were expected to hold in different problems.
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- In this paper, we prove the convexity of trace functionals (A,B,C)mapsto Tr|B^pAC^q|^s,for parameters(p,q,s)that are best possible, whereBandCare anyn-by-npositive definite...
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