Corpus ID: 237605522

Convexity of a certain operator trace functional

@inproceedings{Evert2021ConvexityOA,
  title={Convexity of a certain operator trace functional},
  author={Eric Evert and Scott A. McCullough and Tea vStrekelj and Anna Vershynina},
  year={2021}
}
In this article the operator trace function Λr,s(A)[K,M ] := tr(K ∗ArMArK)s is introduced and its convexity and concavity properties are investigated. This function has a direct connection to several well-studied operator trace functions that appear in quantum information theory, in particular when studying data processing inequalities of various relative entropies. In the paper the interplay between Λr,s and the well-known operator functions Γp,s and Ψp,q,s is used to study the stability of… Expand

References

SHOWING 1-10 OF 31 REFERENCES
Some convexity and monotonicity results of trace functionals
In this paper, we prove the convexity of trace functionals pA,B, Cq ÞÑ Tr|BAC|, for parameters pp, q, sq that are best possible. We also obtain the monotonicity under unital completely positive traceExpand
From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb conjecture
Abstract In this paper we study the joint convexity/concavity of the trace functions Ψ p , q , s ( A , B ) = Tr ( B q 2 K ⁎ A p K B q 2 ) s , p , q , s ∈ R , where A and B are positive definiteExpand
Concavity of certain maps on positive definite matrices and applications to Hadamard products
Abstract If f is a positive function on (0, ∞) which is monotone of order n for every n in the sense of Lowner and if Φ1 and Φ2 are concave maps among positive definite matrices, then the followingExpand
Some Operator and Trace Function Convexity Theorems
We consider convex trace functions $\Phi_{p,q,s} = Trace[ (A^{q/2}B^p A^{q/2})^s]$ where $A$ and $B$ are positive $n\times n$ matrices and ask when these functions are convex or concave. We alsoExpand
Concavity of certain matrix trace and norm functions. II
We refine Epstein's method to prove joint concavity/convexity of matrix trace functions of Lieb type $\mathrm{Tr}\,f(\Phi(A^p)^{1/2}\Psi(B^q)\Phi(A^p)^{1/2})$ and symmetric (anti-) norm functions ofExpand
A Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy II: Convexity and Concavity
AbstractWe revisit and prove some convexity inequalities for trace functions conjectured in this paper’s antecedent. The main functional considered is $$ \Phi_{p,q} (A_1,\, A_2, \ldots, A_m) =Expand
Quantum f-divergences and error correction
TLDR
It is shown that the quantum f-divergences are monotonic under the dual of Schwarz maps whenever the defining function is operator convex, and an integral representation for operator conveX functions on the positive half-line is provided, which is the main ingredient in extending previously known results on the monotonicity inequality and the case of equality. Expand
Sandwiched Rényi divergence satisfies data processing inequality
TLDR
It is shown that sandwiched α-Renyi divergence satisfies the data processing inequality for all values of α > 1, and it is proved that α-Holevo information, a variant of Holevo information defined in terms of sandwichedalpha-renyi divergence, is super-additive. Expand
Convex Trace Functions and the Wigner-Yanase-Dyson Conjecture
Inequalities for quantum divergences and the Audenaert–Datta conjecture
Given two density matrices $\rho$ and $\sigma$, there are a number of different expressions that reduce to the $\alpha$-R\'enyi relative entropy of $\rho$ with respect to $\sigma$ in the classicalExpand
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