  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 non-stabilizer 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.
