Parallel Repetition for Post-Quantum Arguments

In this work, we show that parallel repetition of public-coin interactive arguments reduces the soundness error at an exponential rate even in the post-quantum setting. Moreover, we generalize this result to hold for threshold verifiers, where the parallel repeated verifier accepts if and only if at least $t$ of the executions are accepted (for some threshold $t$). Prior to this work, these results were known only when the cheating prover was assumed to be classical.We also prove a similar result for three-message private-coin arguments. Previously, Bostanci, Qian, Spooner, and Yuen (STOC 2024) proved such a parallel repetition result in the more general setting of quantum protocols, where the verifier and communication may be quantum. We consider only protocols where the verifier is classical, but obtain a simplified analysis, and for the more general setting of threshold verifiers.

@article{huang2025_2506.02277,
  title={ Parallel Repetition for Post-Quantum Arguments },
  author={ Andrew Huang and Yael Tauman Kalai },
  journal={arXiv preprint arXiv:2506.02277},
  year={ 2025 }
}