A Quantum Oracle Separation Between $\mathsf{QMA}(2)$ and $\mathsf{QMA}$

The authors construct a unitary oracle $U$ such that $$\mathsf{QMA}^{U}\neq\mathsf{QMA}(2)^{U}.$$ Their black-box problem is solvable by a $\mathsf{QMA}(2)$ verifier with one oracle query and linear-size unentangled proofs, whereas any $\mathsf{QMA}$ verifier must use either exponentially many queries or an exponentially large witness. As a non-oracle consequence, they prove that for every fixed $\varepsilon,\delta\ge 0$ with $\varepsilon+\delta<1$, any $(\varepsilon,\delta)$-disentangler requires exponentially many input qubits in the number of output qubits, resolving Watrous's no-disentanglers conjecture.

The authors construct a unitary oracle $U$ such that $$\mathsf{QMA}^{U}\neq\mathsf{QMA}(2)^{U}.$$ Their black-box problem is solvable by a $\mathsf{QMA}(2)$ verifier with one oracle query and linear-size unentangled proofs, whereas any $\mathsf{QMA}$ verifier must use either exponentially many queries or an exponentially large witness. As a non-oracle consequence, they prove that for every fixed $\varepsilon,\delta\ge 0$ with $\varepsilon+\delta<1$, any $(\varepsilon,\delta)$-disentangler requires exponentially many input qubits in the number of output qubits, resolving Watrous's no-disentanglers conjecture.