A new preprint posted to arXiv — not yet peer-reviewed — reports a quantum oracle relative to which QMA(2) and QMA are distinct complexity classes. QMA is the quantum analogue of NP, where a quantum verifier checks a single quantum witness; QMA(2) extends this by allowing two unentangled quantum witnesses. Whether the extra witnesses provide genuine computational power has been an open question for roughly two decades.
The authors establish the separation by combining the unitarily invariant polynomial method of She and Yuen with a new construction exploiting projectors onto the symmetric and antisymmetric subspaces. This reduces the QMA lower bound to the well-studied approximate degree of the OR function, a connection that bridges quantum complexity theory and approximation theory. As a corollary, the result resolves the no-disentanglers conjecture posed by Watrous: any circuit that approximately disentangles a bipartite quantum state — an operation central to QMA(2) verification — must receive input exponential in the number of output qubits, for all non-trivial error parameters satisfying ε + δ < 1.
Because oracle separations apply only within relativized models, they do not directly settle the unrelativized QMA versus QMA(2) question, where significant obstacles remain. Nonetheless, oracle results of this kind demarcate the limits of black-box proof techniques and sharpen the structural understanding of quantum witness classes. Independent verification and peer review will be needed to confirm the technical claims.