$α-z$ Bures-Wasserstein量子发散的右均值
Right mean for the $α-z$ Bures-Wasserstein quantum divergence
摘要：
最近，人们提出了一种由$α-z$ Renyi相对熵引起的新的量子发散，称为$α-z$ Bures-Wasserstein量子发散。本文研究了右平均的性质，右平均是$α-z$ Bures-Wasserstein量子发散到每个点的加权和的唯一极小元.给出了右平均与矩阵幂平均包含Cartan平均的许多有趣的算子不等式。利用Wasserstein平均证明了迹不等式，并给出了两个右平均的Hadamard积的界.
英文摘要：
A new quantum divergence induced from the $α-z$ Renyi relative entropy, called the $α-z$ Bures-Wasserstein quantum divergence, has been recently introduced. We investigate in this paper properties of the right mean, which is a unique minimizer of the weighted sum of $α-z$ Bures-Wasserstein quantum divergences to each points. Many interesting operator inequalities of the right mean with the matrix power mean including the Cartan mean are presented. Moreover, we verify the trace inequality with the Wasserstein mean and provide bounds for the Hadamard product of two right means.
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