Toward Separating QMA from QCMA with a Classical Oracle

TL;DR

This paper proposes a novel approach to distinguish QMA from QCMA using a classical oracle, relying on a natural statistical conjecture, advancing understanding in quantum query complexity.

Contribution

It introduces a new method for separating QMA from QCMA with a classical oracle, based on a conjecture with potential broader applications.

Findings

Proposes a new approach to separating QMA and QCMA

Relies on a natural statistical conjecture

Potential implications for quantum query complexity lower bounds

Abstract

QMA is the class of languages that can be decided by an efficient quantum verifier given a quantum witness, whereas QCMA is the class of such languages where the efficient quantum verifier only is given a classical witness. A challenging fundamental goal in quantum query complexity is to find a classical oracle separation for these classes. In this work, we offer a new approach towards proving such a separation that is qualitatively different than prior work, and show that our approach is sound assuming a natural statistical conjecture which may have other applications to quantum query complexity lower bounds.