Computational self-testing for entangled magic states

Can classical systems grasp quantum dynamics executed in an untrusted quantum device? Metger and Vidick answered this question affirmatively by proposing a computational self-testing protocol for Bell states that certifies generation of Bell states and measurements on them. Since their protocol relies on the fact that the target states are stabilizer states, it is highly nontrivial to reveal whether the other class of quantum states, nonstabilizer states, can be self-tested. Among nonstabilizer states, magic states are indispensable resources for universal quantum computation. Here, 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 nonzero magic.