Quantum resource theories have been widely studied to systematically characterize the non-classicality of quantum systems. In this talk, we propose a general resource framework for quantum channels and introducing resource monotones based on general distance quantifiers of channels. We study the interplay between channel and state resource theories by relating resource monotones of a quantum channel to its manipulation power of the state resource. Regarding channels as operational resources, we introduce asymptotic channel distillation and dilution, the most important tasks in an operational resource theory, and show how to bound the conversion rates with channel resource monotones. Furthermore, we extend our framework to the characterization and benchmark of quantum memories. We introduce the robustness of quantum memory, and demonstrate its operational meaning as a resource in three different settings: (1) the resource cost of synthesising the memory with idealised qubit memories, (2) the resource cost of simulating the memory's observational statistics with classical resources, and (3) the performance of the memory in discriminating different input states.
References: arXiv 1904.02680, 1907.02521 (joint work with Xiao Yuan et al.)
Yunchao Liu is a Ph.D. candidate at the division of computer science/EECS, UC Berkeley. He received B.E. from Institute for Interdisciplinary Information Sciences, Tsinghua University in 2019. His research focuses on quantum information and computation.