We present a simple quantum interactive proof (QIP) protocol using the quantum state teleportation (QST) and quantum energy teleportation (QET) protocols. QET is a technique that allows a receiver at a distance to extract the local energy by local operations and classical communication (LOCC), using the energy injected by the supplier as collateral. QET works for any local Hamiltonian with entanglement and, for our study, it is important that getting the ground state of a generic local Hamiltonian is quantum Merlin Arthur (QMA)-hard. The key motivations behind employing QET for these purposes are clarified. Firstly, in cases where a prover possesses the correct state and executes the appropriate operations, the verifier can effectively validate the presence of negative energy with a high probability (Completeness). Failure to select the appropriate operators or an incorrect state renders the verifier incapable of observing negative energy (Soundness). Importantly, the verifier solely observes a single qubit from the prover's transmitted state, while remaining oblivious to the prover's Hamiltonian and state (Zero-knowledge). Furthermore, the analysis is extended to distributed quantum interactive proofs, where we propose multiple solutions for the verification of each player's measurement. The complexity class of our protocol in the most general case belongs to QIP(3)=PSPACE, hence it provides a secure quantum authentication scheme that can be implemented in small quantum communication devices. It is straightforward to extend our protocol to Quantum Multi-Prover Interactive Proof (QMIP) systems, where the complexity is expected to be more powerful (PSPACE$\subset$QMIP=NEXPTIME). In our case, all provers share the ground state entanglement, hence it should belong to a more powerful complexity class QMIP$^*$.

翻译：我们提出了一种基于量子态传输（QST）和量子能量传输（QET）协议的简单量子交互式证明（QIP）协议。量子能量传输是一种技术，允许远距离接收方通过本地操作和经典通信（LOCC）提取局部能量，并以供给方注入的能量作为担保。QET适用于任何具有纠缠的局部哈密顿量，在我们的研究中，重要的是求解一般局部哈密顿量的基态属于量子梅林-亚瑟（QMA）难题。本文阐明了在此类场景下使用QET的关键动机。首先，当证明者持有正确状态并执行适当操作时，验证者能够以高概率有效验证负能量的存在（完备性）。反之，若证明者选择错误的算子或状态，验证者将无法观测到负能量（可靠性）。尤为关键的是，验证者仅能观测到证明者发送状态中的一个量子比特，而无法获知证明者的哈密顿量和状态信息（零知识性）。此外，我们将分析扩展到分布式量子交互式证明，针对每个参与方的测量验证提出了多种解决方案。在最一般情形下，本协议的复杂度类属于QIP(3)=PSPACE，因此该方案适用于小型量子通信设备的量子安全认证。该协议可自然扩展到量子多方交互式证明（QMIP）系统，其复杂度预计更强（PSPACE⊂QMIP=NEXPTIME）。在本方案中，所有证明者共享基态纠缠，因此应属于更强大的复杂度类QMIP$^*$。