A new proof for monotonicity of sandwiched Renyi relative entropy

Abstract:

Itis well known that in quantum information quantum relative is monotonically decreasing under the completely positive and trace-preserving maps. For a new proposed sandwiched R\'enyi quantum relative, a map that is linear trace-preserving and whose Hilber-Schmidt adjoint map satisfies Schwarz inequality, monotonicity still holds. We give a new proof of monotonicity of sandwiched R\'enyi relative entropy for $\alpha\in[\frac{1}{2},1)$. The proof is based on complex interplotation techniques, which already has been used to prove monotonicity under trace-preserving and positive map for $\alpha\in(1,\infty)$.