A quantum oracle separation between QMA(2) and QMA
John Bostanci, Sabee Grewal, Jonas Haferkamp, Andrew Huang, Yeongwoo Hwang, Anand Natarajan, Chinmay Nirkhe
Abstract
We find a quantum oracle relative to which QMA ≠ QMA(2). As a consequence, we resolve the no-disentanglers conjecture of Watrous: for every ε+δ<1, any (ε,δ)-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 QMA lower bound to the approximate degree of OR.
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