A slightly improved upper bound for quantum statistical zero-knowledge

• URL: http://arxiv.org/abs/2512.11597v1
• Date: Fri, 12 Dec 2025 14:33:20 GMT
• Title: A slightly improved upper bound for quantum statistical zero-knowledge
• Authors: François Le Gall, Yupan Liu, Qisheng Wang,
• Abstract summary: The complexity class Quantum Statistical Zero-Knowledge ($mathsfQSZK$) has the best known upper bound $mathsfQIP(2) cap textco-mathsfQIP(2)$.<n>We improve this to $mathsfQIP(2) cap textco-mathsfQIP(2)$ with a quantum linear-space honest prover.<n>Our main techniques are an algorithmic version of the Holevo-Helstrom measurement complexity and the Uhlmann transform, both implementable in quantum linear space
• Score: 11.384500557173867
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The complexity class Quantum Statistical Zero-Knowledge ($\mathsf{QSZK}$), introduced by Watrous (FOCS 2002) and later refined in Watrous (SICOMP, 2009), has the best known upper bound $\mathsf{QIP(2)} \cap \text{co-}\mathsf{QIP(2)}$, which was simplified following the inclusion $\mathsf{QIP(2)} \subseteq \mathsf{PSPACE}$ established in Jain, Upadhyay, and Watrous (FOCS 2009). Here, $\mathsf{QIP(2)}$ 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 $\text{co-}\mathsf{QIP(2)}$ denotes the complement of $\mathsf{QIP(2)}$. We slightly improve this upper bound to $\mathsf{QIP(2)} \cap \text{co-}\mathsf{QIP(2)}$ with a quantum linear-space honest prover. A similar improvement also applies to the upper bound for the non-interactive variant $\mathsf{NIQSZK}$. 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).

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