Interpolation of matrices and matrix-valued densities: The unbalanced case
Interpolation of matrices and matrix-valued densities: The unbalanced case
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DOI：
10.1017/s0956792518000219
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发表时间：
2019-06-01
影响因子：
1.9
通讯作者：
Tannenbaum, Allen
中科院分区：
文献类型：
--
作者：
Chen, Yongxin;Georgiou, Tryphon T.;Tannenbaum, Allen
我们提出了基于描述开放量子系统的Lindblad方程的最优质量输运的量子力学版本的不平衡版本。其中一种是通过Fisher-Rao信息和材料Wasserstein距离的量子力学公式得到的矩阵与矩阵值测度之间的自然插值框架，另一种是Wasserstein距离与Frobenius范数之间的插值框架。对于矩阵值密度度量，我们也给出了类似的结果，即，我们在密度矩阵上添加了空间依赖性。这可以将框架的应用扩展到插值具有不等质量的矩阵值密度/图像。
We propose unbalanced versions of the quantum mechanical version of optimal mass transport that is based on the Lindblad equation describing open quantum systems. One of them is a natural interpolation framework between matrices and matrix-valued measures via a quantum mechanical formulation of Fisher-Rao information and the matricial Wasserstein distance, and the second is an interpolation between Wasserstein distance and Frobenius norm. We also give analogous results for the matrix-valued density measures, i.e., we add a spatial dependency on the density matrices. This might extend the applications of the framework to interpolating matrix-valued densities/images with unequal masses.