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The α-z-Bures Wasserstein divergence

Authors: 

Trung Hoa Dinh, Cong Trinh Le*, Bich Khue Vo, Trung Dung Vuong

Source title: 
Linear Algebra and its Applications, 624: 267-280, 2021 (ISI)
Academic year of acceptance: 
2021-2022
Abstract: 

In this paper, we introduce the α-z-Bures Wasserstein divergence for positive semidefinite matrices A and B as

a

where a is the matrix function in the α-z-Renyi relative entropy. We show that for 0≤ αz ≤ 1, the quantity Φ(A, B) is a quantum divergence and satisfies the Data Processing Inequality in quantum information. We also solve the least squares problem with respect to the new divergence. In addition, we show that the matrix power mean μ(t, A, B)=((1 − t)A+tBp)1/p satisfies the in-betweenness property with respect to the α-z-Bures Wasserstein divergence.