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 (such as the QCMA versus QMA question). However, constructing and proving the security of quantum fire so far has been elusive. Nehoran and Zhandry showed how to construct quantum fire relative to an inefficient quantum oracle (which cannot be instantiated even heuristically). Later, Bostanci, Nehoran, Zhandry gave a candidate construction based on group actions, however, even in the classical oracle model they could only conjecture the security of their scheme, and were not able to give a security proof or argue security.

In this work, for the first time, we give a construction of public-key quantum fire relative to a classical oracle and prove its security unconditionally. Going further, we introduce the functional version of quantum fire called quantum key-fire (akin to quantum money and copy-protection), and we also initiate the study of LOCC security for quantum (key-)fire.

Then, 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: (i) a separation in the computational universe between no-cloning and no-teleportation, (ii) a separation between copy-protection security and unbounded leakage-resilience security (Cakan, Goyal, Liu-Zhang, Ribeiro, TCC’24) and (iii) a separation between computational no-cloning security and computational no-learning security, two security notions introduced recently by Fefferman, Ghosh, Sinha, Yuen (ITCS’26).

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