2025/09/18 by Grewal, Sabee, Kretschmer, William
#Computational Complexity (cs.CC) #FOS: Computer and information sciences #FOS: Physical sciences #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2509.15319
We investigate two resources whose effects on quantum interactive proofs remain poorly understood: the promise of unentanglement, and the verifier's ability to condition on an intermediate measurement, which we call post-measurement branching. We first show that unentanglement can dramatically increase computational power: three-round unentangled quantum interactive proofs equal NEXP, even if only the first message is quantum. By contrast, we prove that if the verifier uses no post-measurement branching, then the same type of unentangled proof system has at most the power of QAM. Finally, we investigate post-measurement branching in two-round quantum-classical proof systems. Unlike the equivalence between public-coin and private-coin classical interactive proofs, we give evidence of a separation in the quantum setting that arises from post-measurement branching.