The model of interactive oracle proofs (IOP) generalizes the notion of probabilistically checkable proof (PCP), in which a static proof is verified probabilistically by querying a small number of bits, to the interactive setting: a polynomial-time verifier interacts with an unbounded prover, but is restricted to only reading a small number of bits, in total, from the messages sent by the prover. IOPs provide a relaxed setting in which to study local probabilistic verification. They have proved instrumental in devising efficient methods for verification through subsequent compilation into non-interactive or succinct protocols. We study a quantum analogue of interactive oracle proofs (qIOP) in which the verifier and communication are both allowed to be quantum; yet the verifier is restricted to perform measurements only on a small number of qubits received from the prover. Our main result is a qIOP for any language in QMA, in which the total communication is polynomial but the verifier only reads a polylogarithmic number of qubits in total. The protocol has completeness parameter exponentially close to $1$ and soundness bounded away from $1$ by a constant. In the absence of a quantum PCP theorem, this provides the first information-theoretically sound local and robust characterization of QMA, albeit interactive. Our protocol combines the use of a quantum locally testable code (LTC) with classical techniques, notably probabilistically checkable proofs of proximity (PCPP). We avoid the necessity for complex multi-qubit tests employed in other settings by leveraging the local indistinguishability property of the quantum LTC.

翻译：交互式预言证明（IOP）模型将概率可检查证明（PCP）的概念推广至交互式设置：在PCP中，静态证明通过查询少量比特以概率方式验证，而IOP中多项式时间验证者与无界证明者交互，但仅从证明者发送的消息中总计读取少量比特。IOP为研究局部概率验证提供了更宽松的环境，并通过后续编译为非交互式或简洁协议，在设计高效验证方法中发挥了关键作用。我们研究交互式预言证明的量子类比（qIOP），其中验证者和通信均允许为量子形式，但验证者仅能对从证明者接收的少量量子比特进行测量。我们的主要结果是：针对QMA中的任意语言，存在一个qIOP协议，其总通信量为多项式级，但验证者仅总计读取多对数数量的量子比特。该协议的完备参数指数趋近于1，而可靠性参数则被常数界限制远离1。在缺乏量子PCP定理的情况下，这首次提供了QMA的基于信息论可靠的局部鲁棒刻画（尽管是交互式的）。我们的协议结合了量子局部可测试码（LTC）与经典技术（特别是概率可检查邻近证明（PCPP））。通过利用量子LTC的局部不可区分性，我们避免了其他设置中复杂多量子比特测试的必要性。