 Hi, I'm Takashi. This is a short abstract video for this work. Non-intractive zero-narration, NISIC, is a protocol to prove validity of some statement without revealing anything beyond its validity in a non-intractive way. We require NISICs to satisfy completeness, soundness, and zero-narrage property. It is easy to see that NISICs for non-trivial languages are impossible in the plain model, so we have to rely on some trusted setup. In this work, we focus on NISICs for QMA with classical verification. Here, QMA is the quantum version of NP or MA where witness and verification can be quantum. Even though we consider such quantum languages, we require that the verification can be done classically, which is a highly non-trivial property. The ultimate goal is to construct classically verifiable NISICs for QMA in the common reference ring model. So far, there is only a heuristic construction and no known construction from standard assumptions. Thus, existing works rely on stronger setup models than the common reference ring model. The motivation of this work is to find new trade-offs among assumptions, security, and models for classically verifiable NISICs for QMA. In this work, we give three constructions of classically verifiable NISICs for QMA with incomparable features. I will explain them one by one. The first construction is in the quantum secret parameter model. In this model, the trusted party first sends a quantum-proving key and classical verification key to the prover and verifier respectively. After this setup, the prover can non-intractively generate a classical proof. We prove that our construction satisfies both statistical soundness and statistical zero-knowledge without assuming any assumption. Note that this is a variant of the NISIC by broadband and griddle or where the proving key is classical, but the proof is quantum. The second construction only requires the trusted setup to generate a common reference ring, but the verifier has to send some instance-independent quantum information to the prover as a setup. After this setup, the prover can non-intractively generate a classical proof. We show that our construction has a dual-mode property under the LW assumption. That is, there are two computational re-indistinguishable modes. One is the binding mode where it satisfies statistical soundness and computational zero-knowledge, and the other is the hiding mode where it satisfies computational soundness and statistical zero-knowledge. Note that the model and assumption are exactly the same as those of Kladangir, Vidic, and Zhen, where they constructed NISICs with computational soundness and computational zero-knowledge. They left it open to make either of them statistical, and we solved this open problem. The third construction is in the bell pair model where the prover and verifier share entanglement as a setup. The bell pair model is often regarded as a quantum analog of the common reference ring model. Our construction satisfies computational soundness and computational zero-knowledge in the quantum random worker model. This answers an open question of Brodovento and Guerrero, who asked if we can construct NISICs for QMA in the bell pair model. This is a comparison table among constructions of classically verifiable NISICs for QMA. For more detail, please attend my talk at Azure Crypt. Thanks.