A general conic optimization solver computes finite-size QKD rates from Rényi entropies more reliably than prior Frank-Wolfe methods.
Concavity of certain matrix trace and norm functions
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We refine Epstein's method to prove joint concavity/convexity of matrix trace functions of the extended Lieb type $Tr{\Phi(A^p)^{1/2}\Psi(B^q)\Phi(A^p)^{1/2}}^s$, where $\Phi$ and $\Psi$ are positive linear maps. By the same method combined with majorization technique, similar properties are proved for symmetric (anti-) norm functions of the form $||{\Phi(A^p)\sigma\Psi(B^q)}^s||$ involving an operator mean $\sigma$. Carlen and Lieb's variational method is also used to improve the convexity property of norm functions $||\Phi(A^p)^s||$.
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quant-ph 2years
2025 2verdicts
UNVERDICTED 2representative citing papers
Large-sample relative majorization of flat state pairs exists exactly when all α-z relative entropies (α<1) are ordered, also giving the optimal conversion rate.
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Finite-size quantum key distribution rates from R\'enyi entropies using conic optimization
A general conic optimization solver computes finite-size QKD rates from Rényi entropies more reliably than prior Frank-Wolfe methods.
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Conditions for Large-Sample Majorization of Pairs of Flat States in Terms of $\alpha$-z Relative Entropies
Large-sample relative majorization of flat state pairs exists exactly when all α-z relative entropies (α<1) are ordered, also giving the optimal conversion rate.