Parallel repetition with a threshold in quantum interactive proofs

Abstract

In this note, we show that $O(\log (1/\epsilon ))$ rounds of parallel repetition with a threshold suffice to reduce completeness and soundness error to $\epsilon$ for single-prover quantum interactive proof systems. This improves on a previous $O(\log (1/\epsilon )\log \log (1/\epsilon ))$ bound from Hornby (2018), while also simplifying its proof. A key element in our proof is a concentration bound from Impagliazzo and Kabanets (2010).