Complete characterization of the additional DREAM resource

Establish a more complete characterization of the additional distributed resource identified by the distributed resource theory of entanglement and magic (DREAM), including its monotones, conversion rates, formation costs, and distillation properties.

Background

The paper introduces DREAM as a unified resource theory whose free states are convex mixtures of product local stabilizer states and whose free operations are local stabilizer operations assisted by classical communication. It proves that DREAM contains states that are simultaneously separable and globally stabilizer, yet resourceful under DREAM, thereby identifying an additional distributed resource not captured by entanglement or magic considered separately.

The paper derives robustness measures for specific two-node and multipartite state families and establishes operational results concerning magic-state teleportation. However, it does not provide a general theory of the newly identified resource: its complete family of monotones, asymptotic conversion rates, formation costs, and distillation capabilities remain to be characterized.