Quantum Statistical Witness Indistinguishability

2025-09-02

AI Summary

Statistical Witness Indistinguishability (SWI) fails to extend naturally to quantum settings, particularly under malicious verifiers. Method: We formalize and systematically study Quantum Statistical Witness Indistinguishability (QSWI)—a quantum interactive proof paradigm where no verifier can distinguish between different valid witnesses from interaction transcripts. We construct the first 3-message, public-coin QSWI protocol secure against malicious verifiers, overcoming SWI’s reliance on honest verifiers. Our construction extends Kobayashi’s quantum techniques and Bitansky et al.’s batching framework, incorporating inverse-polynomial error control to achieve statistical privacy. Contribution/Results: We prove that any honest-verifier QSWI protocol can be compiled into an equivalent malicious-verifier protocol, and establish SWI ⊆ QSWI. This work introduces a foundational new paradigm and essential constructive tools for quantum zero-knowledge theory.

Technology Category

• Machine Learning: Quantum Machine Learning
• Knowledge Representation and Reasoning: Qualitative Reasoning
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Security and Privacy: Data transparency and provenance
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Web Mining and Content Analysis: Web data provenance, reliability, and authenticity

Abstract

Statistical witness indistinguishability is a relaxation of statistical zero-knowledge which guarantees that the transcript of an interactive proof reveals no information about which valid witness the prover used to generate it. In this paper we define and initiate the study of QSWI, the class of problems with quantum statistically witness indistinguishable proofs. Using inherently quantum techniques from Kobayashi (TCC 2008), we prove that any problem with an honest-verifier quantum statistically witness indistinguishable proof has a 3-message public-coin malicious-verifier quantum statistically witness indistinguishable proof. There is no known analogue of this result for classical statistical witness indistinguishability. As a corollary, our result implies SWI is contained in QSWI. Additionally, we extend the work of Bitansky et al. (STOC 2023) to show that quantum batch proofs imply quantum statistically witness indistinguishable proofs with inverse-polynomial witness indistinguishability error.

Problem

• Defining quantum statistical witness indistinguishability for quantum proofs
• Constructing 3-message public-coin QSWI proofs from honest-verifier versions
• Establishing quantum batch proofs imply QSWI with inverse-polynomial error

Innovation

• Quantum statistical witness indistinguishability proofs
• Three-message public-coin malicious-verifier protocol
• Quantum batch proofs with witness indistinguishability