A quantum oracle separation between QMA(2) and QMA

Abstract

We find a quantum oracle relative to which $\mathsf{QMA} \neq \mathsf{QMA}(2)$. As a consequence, we resolve the no-disentanglers conjecture of Watrous: for every $\epsilon+\delta<1$, any $(\epsilon,\delta)$-disentangler requires input size exponential in the number of output qubits. Our proof combines the unitarily invariant polynomial method of She and Yuen (ITCS'23) with a new construction based on the symmetric and antisymmetric subspace projectors, reducing the $\mathsf{QMA}$ lower bound to the approximate degree of $\mathrm{OR}$.