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Convexity of quantum $��^2$-divergence
Description
The quantum ��^2-divergence has recently been introduced and applied to quantum channels (quantum Markov processes). In contrast to the classical setting the quantum ��^2-divergence is not unique but depends on the choice of quantum statistics. In the reference [11] a special one-parameter family of quantum ��^2_��(��,��)-divergences for density matrices were studied, and it was established that they are convex functions in (��,��) for parameter values ��\in [0,1], thus mirroring the classical theorem for the ��^2(p,q)-divergence for probability distributions (p,q). We prove that any quantum ��^2-divergence is a convex function in its two arguments.
Proof clarified, typos corrected
