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) 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