Parallel repetition with a threshold in quantum interactive proofs

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