Unified robustness of general quantum resources of a quantum system

Abstract Treating robustness as a key measure for various quantum resources, this work proposes a general quantum resource theory (GQRT) for a quantum system (GQRT4QS), which was formally a pair consisting of a free-state set and a free-operation set. Here, the free-state set whose elements are called free states is defined as any compact convex set of quantum states of a quantum system that includes the maximally random state, while the free-operation set whose elements are called free operations is a semigroup consisting of quantum operations of the system that map free states to free states. Within this GQRT4QS framework, we first introduce the unified robustness of quantum resources and rigorously prove its validity as a quantum resource measure. Subsequently, we define the unified geometric robustness of quantum resources and further demonstrate that it also satisfies the criteria for a valid quantum resource measure. For practical applications, we derive a series of resource-specific robustness measures, encompassing the robustness and geometric robustness of entanglement, Bell nonlocality, Einstein-Podolsky-Rosen (EPR) steering, and quantum coherence.