Zero-knowledge and multi-prover systems are both central notions in classical and quantum complexity theory. There is, however, little research in quantum multi-prover zero-knowledge systems. This paper studies complexity-theoretical aspects of the quantum multi-prover zero-knowledge systems. This paper has two results: 1.QMIP* systems with honest zero-knowledge can be converted into general zero-knowledge systems without any assumptions. 2.QMIP* has computational quantum zero-knowledge systems if a natural computational conjecture holds. One of the main tools is a test (called the GHZ test) that uses GHZ states shared by the provers, which prevents the verifier's attack in the above two results. Another main tool is what we call the Local Hamiltonian based Interactive protocol (LHI protocol). The LHI protocol makes previous research for Local Hamiltonians applicable to check the history state of interactive proofs, and we then apply Broadbent et al.'s zero-knowledge protocol for QMA \cite{BJSW} to quantum multi-prover systems in order to obtain the second result.
翻译:经典和量子复杂理论中,零知识和多源系统都是核心概念。 然而,在量子多源零知识系统中,几乎没有什么研究。 本文研究量子多源零知识系统的复杂性理论方面。 本文有两个结果: 1. QMIP* 系统, 具有诚实的零知识, 可以不经任何假设而转换为普通的零知识系统。 2. QMIP* 如果自然计算假设存在, 则拥有计算量零知识系统。 其中一项主要工具是测试( 称为 GHZ 测试), 使用验证人共享的GHZ 状态, 防止验证人在上述两个结果中发动攻击。 另一个主要工具是我们称之为以本地汉密尔顿为基础的互动协议( LHI 协议) 。 LHIP 协议将适用于本地汉密尔顿人用于检查交互证据历史状态的先前研究, 然后我们对量子多源系统应用Broadbent 等的零知识协议, 以获取第二个结果。