日時
2020年6月17日16:00 - 18:10
講演者
相馬 輔 (東京大学 大学院情報理工学系研究科 助教)
会場
via Zoom
言語
英語

Matrix scaling is a classical problem with a wide range of applications. It is known that the Sinkhorn algorithm for matrix scaling is interpreted as alternating e-projections from the viewpoint of classical information geometry.

Recently, a generalization of matrix scaling to completely positive maps called operator scaling has been found to appear in various fields of mathematics and computer science, and the Sinkhorn algorithm has been extended to operator scaling.

In this study, the operator Sinkhorn algorithm is studied from the viewpoint of quantum information geometry through the Choi representation of completely positive maps. The operator Sinkhorn algorithm is shown to coincide with alternating e-projections with respect to the symmetric logarithmic derivative metric, which is a Riemannian metric on the space of quantum states relevant to quantum estimation theory. This talk is based on joint work with Takeru Matsuda.

*Please contact Keita Mikami's mail address to get access to the Zoom meeting room.

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