Quantum fire is a distribution of quantum states that can be efficiently cloned, but cannot be efficiently converted into a classical string. First considered by Nehoran and Zhandry (ITCS'24) and later formalized by Bostanci, Nehoran, Zhandry (STOC'25), quantum fire has strong applications and implications in cryptography, along with important connections to physics and complexity. However, constructing and proving the security of quantum fire so far has been elusive. Nehoran and Zhandry gave a construction relative to an inefficient quantum oracle. Later, Bostanci et al gave a candidate construction based on group actions, however, even in the oracle model they could only conjecture the security of their scheme, and were not able to prove security. In this work, we give a construction of public-key quantum fire relative to a classical oracle and prove its security unconditionally. Going further, we introduce two stronger notions that generalize it: Quantum key-fire where the clonable fire states serve as keys, and interactive (i.e. LOCC) security for quantum (key-)fire. We give a construction of quantum key-fire relative to a classical oracle and unconditionally prove that it satisfies interactive security for any unlearnable functionality. As a result, we also obtain the first classical oracle separations between various notions in physics and cryptography: *** A computational separation between two fundamental principles of quantum mechanics: No-cloning and no-teleportation, which are equivalent in information-theoretically. *** A separation between copy-protection security (Aaronson, CCC'09) and LOCC leakage-resilience security (Cakan, Goyal, Liu-Zhang, Ribeiro, TCC'24). *** A separation between computational no-cloning security and no-learning security, two notions introduced recently by Fefferman, Ghosh, Sinha, Yuen (ITCS'26).

翻译：量子火是一种量子态分布，它可以被高效克隆，但无法高效转换为经典字符串。该概念最初由Nehoran和Zhandry（ITCS'24）提出，后经Bostanci、Nehoran、Zhandry（STOC'25）形式化定义。量子火在密码学中具有重要的应用价值和理论意义，同时与物理学及复杂性理论存在深刻联系。然而，量子火的构造及其安全性证明至今仍具挑战性。Nehoran和Zhandry曾提出基于低效量子预言机的构造方案；随后Bostanci等人给出了基于群作用的候选构造，但即使在预言机模型下，其方案的安全性仍仅为猜想而未能得到证明。本文提出一种基于经典预言机的公钥量子火构造方案，并给出其无条件安全性证明。进一步地，我们引入两个更具一般性的强化概念：以可克隆火态作为密钥的量子密钥火，以及量子（密钥）火的交互式（即LOCC）安全性。我们构建了基于经典预言机的量子密钥火方案，并无条件证明其对任意不可学习功能均满足交互式安全性。由此，我们首次在经典预言机模型下实现了物理学与密码学中若干重要概念的分离：*** 量子力学两大基本原理——信息论意义上等价的无克隆定理与无隐形传态定理——在计算复杂性层面的分离；*** 复制保护安全性（Aaronson, CCC'09）与LOCC防泄漏安全性（Cakan, Goyal, Liu-Zhang, Ribeiro, TCC'24）的分离；*** 最近由Fefferman、Ghosh、Sinha、Yuen（ITCS'26）提出的计算无克隆安全性与无学习安全性两个概念的分离。