Quantum catalysis The power of catalytic local operations: State transformations and activation of Bell nonlocality Unitary discrimination Unitary channel discrimination beyond group structure: Advantages of sequential and indefinite-causal-order strategies Channel discrimination Strict hierarchy between parallel, sequential, and indefinite-causal-order strategies for channel discrimination High-dim entanglement Measurements in two bases are sufficient for certifying high-dimensional entanglement Measurement incompatibility Most incompatible measurements for robust steering tests