부산대학교 도서관

In recent years, there has been active research toward understanding the connection between symmetry and physics from the viewpoint of quantum information theory. This approach stems from the resource theory of asymmetry (RTA), a general framework treating quantum dynamics with symmetry, and scopes various fields ranging from the fundamentals of physics, such as thermodynamics and black hole physics, to the limitations of information processing, such as quantum computation, quantum measurement, and error-correcting codes. Despite its importance, in RTA, the resource measures characterizing the asymptotic conversion rate between i.i.d. states are not known except for $U(1)$ and $\mathbb Z_2$. In this letter, we solve this problem for the finite group symmetry and partially solve for the compact Lie group symmetry. For finite groups, we clarify that (1) a set of resource measures characterizes the optimal rate of the exact conversion between i.i.d. states in arbitrary finite groups, and (2) when we consider the approximate conversion with vanishingly small error, we can realize arbitrary conversion rate between almost arbitrary resource states. For Lie group symmetry, we show that the optimal rate of the i.i.d. state conversion with vanishingly small error is bounded by the ratio of the Fisher information matrices. We give a conjecture that the Fisher information matrices also characterize the optimal conversion rate, and illustrate the reasoning. These results are expected to significantly broaden the scope of the application of RTA.
Comment: 13 pages. The contents of this paper were presented as a contribution talk at Quantum Resources 2023 on December 14 by one of the authors, and its video was uploaded to YouTube on December 25 (link: https://www.youtube.com/watch?v=cGGkdC9MXi8). This manuscript is to present our results on arXiv along with the upload of the video. The contents will be updated in the next version