2023/06/23 by Bassirian, Roozbeh, Fefferman, Bill, Marwaha, Kunal · 1 citation
#Computational Complexity (cs.CC) #FOS: Computer and information sciences #FOS: Physical sciences #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2306.13247
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.