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arXiv · 2306.13247

Quantum Merlin-Arthur and proofs without relative phase

Roozbeh Bassirian·Bill Fefferman·Kunal Marwaha
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Abstract

We study a variant of QMA where quantum proofs have no relative phase (i.e. non-negative amplitudes, up to a global phase). If only completeness is modified, this class is equal to QMA [arXiv:1410.2882]; but if both completeness and soundness are modified, the class (named QMA+ by Jeronimo and Wu) can be much more powerful. We show that QMA+ with some constant gap is equal to NEXP, yet QMA+ with some *other* constant gap is equal to QMA. One interpretation is that Merlin's ability to "deceive" originates from relative phase at least as much as from entanglement, since QMA(2) $\subseteq$ NEXP.

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Roozbeh Bassirian, Bill Fefferman, Kunal Marwaha. 2023-06-23. Quantum Merlin-Arthur and proofs without relative phase. https://arxiv.org/abs/2306.13247

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