主题：One-shot operational quantum resource theory, with applications to quantum computation
Zi-Wen Liu is currently a postdoctoral fellow at Perimeter Institute for Theoretical Physics in Canada. He obtained a PhD in Theoretical Physics from MIT in 2018. He is broadly interested in quantum information and computation, and their connections to quantum gravity and condensed matter physics.
A fundamental approach for the characterization and quantification of all kinds of resources is to study the conversion between different resource objects under certain constraints. Here we analyze, from a resource-non-specific standpoint, the optimal efficiency of resource formation and distillation tasks with only finite copies of the given quantum state, thereby establishing a unified framework of one-shot quantum resource manipulation. We find general bounds on the optimal rates characterized by resource measures based on the smooth max/min-relative entropies and hypothesis testing relative entropy, as well as the free robustness measure, providing them with general operational meanings in terms of optimal state conversion. We also present a series of no-go theorems for resource distillation, from which we can understand the fundamental limits to the efficiency of distillation-type tasks, a crucial problem for quantum information and computation. Our general results encompass a wide class of resource theories such as entanglement, coherence, superposition, magic states, asymmetry, and thermal non-equilibrium, via the theory-dependent coefficients we introduce. Lastly, we give some basic examples on how to use our general results to obtain several interesting new understandings of the magic state model and the cost of fault-tolerant quantum computation, which are key topics in quantum computation.
Based on [PRL 123, 020401 (2019)] and several forthcoming works.