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arXiv · 2610.06760

A classical oracle separation between QMA and QMA(2)

Sabee Grewal·Saachi Mutreja·Kabir Tomer
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Abstract

We exhibit a classical oracle relative to which QMA \neq QMA(2). The separation is based on a separable Hamiltonian problem defined by signed edge constraints on a graph. The YES instances have zero-energy product states, while the NO instances, constructed using the antisymmetric subspace, have entangled zero-energy states but no low-energy product states. For the QMA lower bound, we use compressed-oracle techniques to track the information learned by a quantum computation making few queries to a YES instance. The key step is to map the resulting superpositions of partial oracle records to the NO family without significantly changing the verifier's behavior.

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Sabee Grewal, Saachi Mutreja, Kabir Tomer. 2026-10-05. A classical oracle separation between QMA and QMA(2). https://arxiv.org/abs/2610.06760

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