Resource theory of nonrevivals with applications to quantum many-body scars

The study of state revivals has long advanced our understanding of dynamical systems. We introduce a resource theory framework to study the use of state revivals in quantum information. In this theory, a state is said to contain no amount of resource if it experiences perfect revivals under some unitary evolution. All other states are said to be resourceful. The resource, which we dub ``nonrevivals,'' quantifies a state's inability to experience revivals. We use our framework to understand revivals in quantum many-body scarred systems and their applications. In particular, we show that quantum many-body scarred dynamics can produce revivals in the Hayden-Preskill decoding protocol and can also be used to recover damaged quantum information. We also use our resource theory to bound information scrambling. Our theory establishes a framework to study information retrieval and its applications in quantum many-body physics.