A slightly improved upper bound for quantum statistical zero-knowledge

François Le Gall; Yupan Liu; Qisheng Wang

Paper

A slightly improved upper bound for quantum statistical zero-knowledge

Abstract

The complexity class Quantum Statistical Zero-Knowledge (

), introduced by Watrous (FOCS 2002) and later refined in Watrous (SICOMP, 2009), has the best known upper bound

, which was simplified following the inclusion

established in Jain, Upadhyay, and Watrous (FOCS 2009). Here,

denotes the class of promise problems that admit two-message quantum interactive proof systems in which the honest prover is typically \textit{computationally unbounded}, and

denotes the complement of

. We slightly improve this upper bound to

with a quantum linear-space honest prover. A similar improvement also applies to the upper bound for the non-interactive variant

. Our main techniques are an algorithmic version of the Holevo-Helstrom measurement and the Uhlmann transform, both implementable in quantum linear space, implying polynomial-time complexity in the state dimension, using the recent space-efficient quantum singular value transformation of Le Gall, Liu, and Wang (CC, to appear).