SandwichedRenyi量子相对熵单调性的另一证明

摘要

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Sandw iched Renyi量子相对熵,当映射满足Schw arz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∈12,1)时Sandw iched 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.%It is well known that quantum relative entropy is monotonically decreasing under the complete-ly positive and trace-preserving maps.For a new proposed sandwiched Renyi quantum relative entropy, the monotonicity still holds under the linear trace-preserving map w hose Hilber-Schmidt adjoint map sat-isfies Schwarz inequality.In this paper,we give a new proof for the monotonicity of the sandwiched Re-nyi relative entropy for α∈[12,1).T he proof is based on the complex interpolation techniques,w hich is used to prove the monotonicity under the trace-preserving and positive map for α ∈(1,∞).