Class Description

QMA⁺: QMA With Non-Negative Amplitudes

Same as QMA, except now the witness must contain a state with non-negative amplitudes in the computational basis.

This class is sensitive to completeness-soundness gap, as proved in [BFM23]: At some constant gap, it is equal to QMA; at another constant gap, it is equal to NEXP.

Defined in [JW23].

Linked From

QMA⁺(2): QMA(2) With Non-Negative Amplitudes

Same as QMA(2), except now *each* witness must contain a state with non-negative amplitudes in the computational basis.

This class was defined in [JW23] as a possible approach to prove QMA(2) equals NEXP. QMA⁺(2) at some completeness-soundness gap is equal to QMA(2), but at another constant gap, it is equal to NEXP. As of 2025 this problem is still open.

See also QMA⁺.

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