The general quantum χ2-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 χ2-divergence is not unique, as opposed to the classical χ2-divergence, but depends on the choice of quantum statistics. It was noticed that the elements in a particular one-parameter family χα2(ρ,σ) of quantum χ2-divergences are convex functions in the density matrices (ρ,σ), thus mirroring the convexity of the classical χ2(p,q)-divergence in probability distributions (p,q). We prove that any quantum χ2-divergence is a convex function in its two arguments.
|Number of pages||3|
|Journal||Proceedings of the National Academy of Sciences of the United States of America|
|Publication status||Published - 2011 Jun 21|
- Monotone metric
- Operator monotone function
- Quantum mechanics
ASJC Scopus subject areas