Limitations of Classically Simulable Measurements for Quantum State Discrimination

In the realm of fault-tolerant quantum computing, stabilizer operations play a pivotal role, characterized by their remarkable efficiency in classical simulation. This efficiency sets them apart from nonstabilizer operations within the quantum computational theory. In this Letter, we investigate the limitations of classically simulable measurements in distinguishing quantum states. We demonstrate that any pure magic state and its orthogonal complement of odd prime dimensions cannot be unambiguously distinguished by stabilizer operations, regardless of how many copies of the states are supplied. We also reveal intrinsic similarities and distinctions between the quantum resource theories of magic states and entanglement in quantum state discrimination. The results emphasize the inherent limitations of classically simulable measurements and contribute to a deeper understanding of the quantum-classical boundary.