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The main goal of the project is to establish useful approaches to describe the resources contained in quantum processes (quantum channels and more general higher-order quantum transformations) and to understand the advantages that they can provide in different settings.
During this early phase of the project, we focused on two tasks: (1) finalizing some research developments that began before the JSPS project started, but are directly related to the topic of the project; (2) exploring new mathematical methods and approaches in the study of quantum resources.
With regards to point (1), this led to a publication ["One-shot yield-cost relations in general quantum resource theories", PRX Quantum 3, 010348 (2022)] and another paper which is currently in preparation with collaborators. In particular, the published work is concerned with improved bounds for the conversion of quantum resources in noisy settings, which includes also transformations of resources of quantum channels.
For point (2), we have managed to establish a new approach to the characterization of quantum resources of quantum states, which is able to overcome the limitations of many previous methods and to tightly describe the capabilities of stochastic (probabilistic) resource transformations. This result was published ["Probabilistic transformations of quantum resources", Physical Review Letters 128, 110505 (2022)] and presented as a talk at the international conference Quantum Information Processing (QIP) 2022.