Probe of generic quantum contextuality and nonlocality resources for qubits

We reveal that the entropic uncertainty relation with a quantum memory is able to intrinsically connect local generic contextuality addressed in the pioneering work by Spekkens and nonlocal quantum resources such as entanglement and Bell nonlocality. Based on the constructed optimal set for any given single-qubit state, we prove rigorously a faithful criterion to witness the generic contextuality in the scenario of local quantum state preparation. Furthermore, within the framework of quantum resource distribution, it is proved that there exist quantitative trade-off relations between local preparation contextuality and bipartite entanglement or Bell nonlocality in a shared quantum system, which are captured by two inequalities where the local and nonlocal quantum resources can coexist. The faithful criterion and quantitative inequalities are all experimentally testable, which are verified through two independent well-designed experiments on the Quafu quantum cloud platform.