Sandwiched Renyi 量子相对熵单调性的另一证明

A new proof for monotonicity of sandwiched Renyi relative entropy

摘要:

已知量子信息中的量子相对熵在保迹完全正定的映射作用下是单调递减的。对于一种新提出的sandwiched R\'enyi量子相对熵，也已证明当映射满足薛瓦兹不等式或映射是保迹正定时，该量子相对熵的单调性也成立。我们给出$\alpha\in[\frac{1}{2},1)$时sandwiched R\'enyi量子相对熵单调性的另一证明，证明方法用到了复插值技巧，这个技巧曾经运用于证明$\alpha\in(1,\infty)$时量子相对熵在保迹正定映射的作用下也满足单调性。

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