2011/02/20 by Frank Hansen · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Mathematical Inequalities and Applications #Quantum Information and Cryptography #Statistical Mechanics and Entropy #math-ph #math.MP
paper · pdf · doi:10.1073/pnas.1106423108
published as Proc Natl Acad Sci USA 108:10078-10080 (2011) · Proof clarified, typos corrected
arxiv created 2011/02/20 · openalex publication_date 2011/06/03 · arxiv updated 2012/10/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The general quantum χ(2)-divergence has recently been introduced by Temme et al. [Temme K, Kastoryano M, Ruskai M, Wolf M, Verstrate F (2010) J Math Phys 51:122201] and applied to quantum channels (quantum Markov processes). The quantum χ(2)-divergence is not unique, as opposed to the classical χ(2)-divergence, but depends on the choice of quantum statistics. It was noticed that the elements in a particular one-parameter family of quantum χ(2)-divergences are convex functions in the density matrices (ρ,σ), thus mirroring the convexity of the classical χ(2)(p,q)-divergence in probability distributions (p,q). We prove that any quantum χ(2)-divergence is a convex function in its two arguments.