Sandwiched Renyi 量子相对熵单调性的另一证明

量子相对熵在保迹完全正定的映射作用下是单调递减的.此外,对于一种新提出的Sandwiched Renyi量子相对熵,当映射满足Schwarz不等式或映射保迹正定时,也有研究证明该量子相对熵的单调性也成立.本文利用复插值技巧给出当α∈1/2,1)时Sandwiched Renyi量子相对熵单调性的另一证明.该技巧曾被用于证明α∈(1,∞)时量子相对熵在保迹正定映射的作用下满足单调性.

A new proof for monotonicity of sandwiched Renyi relative entropy

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 $\alpha\in(1,\infty)$.