English

Quantum Merlin-Arthur and proofs without relative phase

Quantum Physics 2023-06-26 v1 Computational Complexity

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.

Cite

@article{arxiv.2306.13247,
  title  = {Quantum Merlin-Arthur and proofs without relative phase},
  author = {Roozbeh Bassirian and Bill Fefferman and Kunal Marwaha},
  journal= {arXiv preprint arXiv:2306.13247},
  year   = {2023}
}

Comments

18 pages, 2 figures

R2 v1 2026-06-28T11:12:26.857Z