Computational self-testing for entangled magic states

TL;DR

This paper extends the concept of computational self-testing to non-stabilizer states, specifically magic states for quantum gates, demonstrating that some can be self-tested while others cannot, impacting quantum verification methods.

Contribution

It introduces a method to self-test certain non-stabilizer magic states, notably for the CCZ gate, advancing quantum device verification beyond stabilizer states.

Findings

CCZ magic state can be self-tested.

T gate magic state cannot be self-tested.

Applicable to proofs of quantumness for state verification.

Abstract

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.