  In the seminal paper [Metger and Vidick, Quantum '21], they proposed a
computational self-testing protocol for Bell states in a single quantum device.
Their protocol relies on the fact that the target states are stabilizer states,
and hence it is highly non-trivial to reveal whether the other class of quantum
states, non-stabilizer states, can be self-tested within their framework. Among
non-stabilizer states, magic states are indispensable resources for universal
quantum computation. In this letter, we show that a magic state for the CCZ
gate can be self-tested while that for the T gate cannot. Our result is
applicable to a proof of quantumness, where we can classically verify whether a
quantum device generates a quantum state having non-zero magic.
