发表机构
Technische Universität Wien; The University of Tokyo（维也纳工业大学; 东京大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种基于能量消耗的热力学量子性证明，利用无结构随机预言机下的搜索问题，证明经典机器需指数级熵产生，而量子机器仅需多项式能量，从而以低能耗认证量子性。
AI 中文摘要
证明一台机器执行了真正的量子操作是量子信息处理中的一个核心挑战。现有的量子性证明通常依赖于在计算复杂性假设（如计算困难性）或对经典运行时间、内存或预言机查询次数的显式限制下，经典机器无法完成的计算任务。在此，我们引入一种替代范式：基于能量消耗的热力学量子性证明。利用Yamakawa和Zhandry的搜索问题，并采用无结构的均匀随机预言机，我们证明任何以恒定成功概率解决该任务的经典机器必须产生随安全参数指数增长的熵。根据兰道尔原理，这暗示了热耗散指数级下界，进而对任何循环经典实现给出了能量消耗的指数下界。相比之下，相应的量子证明者以多项式查询和门复杂度解决该任务，在量子实现的标准假设下给出多项式能量消耗。因此，在随机预言机设置中，成功实现中足够低的能量消耗通过宏观热力学观察能量消耗来认证量子性。
英文摘要
Demonstrating that a machine performs genuinely quantum operations is a central challenge in quantum information processing. Existing proofs of quantumness typically rely on computational tasks that are infeasible for classical machines under assumptions such as computational hardness, or explicit bounds on classical runtime, memory, or oracle queries. Here we introduce an alternative paradigm: a thermodynamic proof of quantumness based on energy consumption. Using the search problem of Yamakawa and Zhandry with a structureless uniformly random oracle, we show that any classical machine solving the task with constant success probability must generate entropy that grows exponentially with the security parameter. By Landauer's principle, this implies an exponential lower bound on heat dissipation and hence on the energy consumption of any cyclic classical implementation. In contrast, the corresponding quantum prover solves the task with polynomial query and gate complexity, giving polynomial energy consumption under standard assumptions for quantum implementations. Thus, in the random-oracle setting, sufficiently low energy consumption in a successful implementation certifies quantumness through a macroscopic thermodynamic observation of energy consumption.
Comments6 + 16 pages, 4 figures, comments welcome
