Parallel repetition with a threshold in quantum interactive proofs

TL;DR

This paper improves the bounds on the number of rounds needed in parallel repetition with a threshold to reduce errors in single-prover quantum interactive proofs, simplifying previous proofs and using a concentration bound.

Contribution

It establishes that only logarithmic rounds are needed, improving previous bounds and simplifying the proof methodology for quantum interactive proof systems.

Findings

Reduced the number of rounds to O(log(1/ε)) for error reduction.

Simplified the proof of parallel repetition bounds.

Utilized a concentration bound from Impagliazzo and Kabanets (2010).

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).