Title: A theory of resource destruction

Abstract: Resource theory is a widely-applicable framework for analyzing the physical resources required for given tasks, such as computation, communication, and energy extraction. In this talk, we propose a general scheme for studying and understanding resource theories based on resource-destroying maps, which leave resource-free states unchanged but erase the resource stored in all other states. In particular, we introduce a group of simple conditions for the class of resource-free operations, which plays a key role in the general framework of resource theories. Our theory reveals fundamental connections among free states, free operations and resource measures. We explicitly discuss our theory in the contexts of coherence and discord to illustrate properties of resource destruction.