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arXiv:2610.03593

Quantum Fire with Delegated Cloning

Rohit Chatterjee, Ananta Mukherjee, Vir Pathak, Supartha Podder

quant-phcs.CRSubmitted Oct 2, 2026• Announced Oct 5, 2026• 0 citations• Revised Oct 5, 2026 (v2)
v1 · Oct 2, 2026v2 · Oct 5, 2026
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Abstract

Quantum fire is a recently introduced cryptographic primitive consisting of efficiently preparable quantum states, called \emph{flames}, that admit efficient cloning but resist efficient telegraphing, namely reconstruction via classical communication without preshared entanglement. In all prior constructions of quantum fire, cloning is a public operation that requires no separate key and every holder of a flame state can clone it. For applications to access control, however, an issuer may wish to delegate cloning to designated quantum servers while withholding this capability from other flame holders. To address this, we introduce \emph{delegatable quantum fire}, in which cloning requires a separate key. We give two constructions in the classical-oracle model. Our first construction uses a classical secret key which enables cloning, and any user with the entire key may clone successfully. Our second construction, which we call \emph{torch-fire}, uses quantum cloning keys, called \emph{torches}, which enable cloning while remaining unaffected in the process but cannot otherwise be split or delegated to enable additional cloning. An efficient adversary given $m$ torches cannot, except with negligible probability, enable more than $m$ noncommunicating parties to each clone a fresh, independently issued challenge flame. The adversary may jointly process its resources before separating the parties and distribute arbitrarily entangled registers among them. Both constructions are in the oracle model, relying on public classical oracles that allow queries in quantum superposition.

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Quantum fire is a recently introduced cryptographic primitive consisting of efficiently preparable quantum states, called \emph{flames}, that admit efficient cloning but resist efficient telegraphing, namely reconstruction via classical communication without preshared entanglement. In all prior constructions of quantum fire, cloning is a public operation that requires no separate key and every holder of a flame state can clone it. For applications to access control, however, an issuer may wish to delegate cloning to designated quantum servers while withholding this capability from other flame holders. To address this, we introduce \emph{delegatable quantum fire}, in which cloning requires a separate key.
We give two constructions in the classical-oracle model. Our first construction uses a classical secret key which enables cloning, and any user with the entire key may clone successfully. Our second construction, which we call \emph{torch-fire}, uses quantum cloning keys, called \emph{torches}, which enable cloning while remaining unaffected in the process but cannot otherwise be split or delegated to enable additional cloning. An efficient adversary given mmm torches cannot, except with negligible probability, enable more than mmm noncommunicating parties to each clone a fresh, independently issued challenge flame. The adversary may jointly process its resources before separating the parties and distribute arbitrarily entangled registers among them. Both constructions are in the oracle model, relying on public classical oracles that allow queries in quantum superposition.
Quantum fire consists of quantum states that can be efficiently functionally cloned but cannot be transmitted using one-way classical communication. Whereas all previous quantum-fire constructions with proven untelegraphability are relative to an oracle, ours, based on one-shot signatures, is in the standard model. Our construction achieves two further notions that we introduce: (a) keyless untelegraphability, a strengthening of untelegraphability; and (b) conversability, meaning that a flame, though not telegraphable via one-way classical communication, can be transmitted via classical interaction. Hence one-way and two-way classical communication differ qualitatively in their power to transmit this quantum fire. We use these two novel properties of quantum fire, along with its clonability, to give one of the first cryptographic applications of quantum fire. Keyless untelegraphability forces the distribution of serial numbers of valid flames to have high min-entropy, while conversability and clonability allow the corresponding flame to be cloned and transferred using only classical communication. We present two variants of our conversable quantum-fire construction. The first, based on one-shot signatures (instantiable from subexponential iO, subexponentially secure one-way functions, and LWE), supports polynomially many flames, and super-logarithmic min-entropy of the serial-number distribution. The second, under the stronger assumption of exponentially unforgeable one-shot signatures (instantiable relative to a classical oracle), supports exponentially many flames, and linear min-entropy.
Aaronson, Atia, and Susskind (2020) established that efficiently mapping between quantum states ∣ψ⟩|ψ\rangle∣ψ⟩ and ∣ϕ⟩|ϕ\rangle∣ϕ⟩ is computationally equivalent to distinguishing their superpositions ∣ψ⟩±∣ϕ⟩|ψ\rangle \pm |ϕ\rangle∣ψ⟩±∣ϕ⟩. We generalize this insight into a broader duality principle, wherein manipulating quantum states in one basis is equivalent to extracting their value in a complementary basis. This general duality principle states that the ability to implement a unitary representation of a group is computationally equivalent to the ability to perform a Fourier subspace extraction from its irreducible representations. Building on our duality principle, we present the following applications: * We extend the construction of publicly-key quantum money of Zhandry (2024) from Abelian group actions to a construction of quantum lightning from non-Abelian group actions, and eliminate Zhandry's reliance on a black-box model for justifying security. Instead, we prove a direct reduction to a computational assumption -- the pre-action security of cryptographic group actions. Our construction is realizable with symmetric group actions, including those implicit in the McEliece cryptosystem. * We provide an alternative quantum lightning construction from one-way homomorphisms, with security holding under certain conditions. This scheme shows equivalence among four security notions: quantum lightning security, worst-case and average-case cloning security, and security against preparing a canonical state. * We formalize the notion of quantum fire, states that are efficiently clonable, but not efficiently telegraphable. These states can be spread like fire, provided they are kept alive quantumly and do not decohere. The only previously known construction relied on a unitary quantum oracle, whereas we present the first candidate construction of quantum fire using a classical oracle.
Quantum computers can make use of quantum mechanics to achieve surprising speed-ups relative to classical computers, for important computational problems. Quantum computers are gradually coming into reality, but the current implementations are big, require advanced facilities and could only be used as a cloud service in the foreseeable future. If we want to run quantum computations on secret data, we require protocols for performing computations on a remote quantum server without leaking information to the server about the data being processed. In the quantum computation delegation problem, a client with limited quantum computing resources wishes to evaluate a secret quantum circuit C with the help of a more powerful remote server. The protocol is deemed secure if the server learns nothing about either the circuit or the input state even if the server acts maliciously. This problem, first raised in (Childs05), has become fundamental to the study of quantum cryptography, because of its practical importance, and because it provides a testbed for new techniques that can be later applied to related problems (for example, quantum computation verification [FK12]). Prior to our work, known protocols for this problem were either proven secure against all possible attackers, without any complexity-theoretic assumptions, but highly inefficient for the client; or efficient but proven secure only based on strong cryptographic assumptions. This second category of protocols is only secure if there exist public-key encryption schemes that are secure against quantum attacks and that have special additional properties. Very few candidates for such schemes are known, and their security remains poorly understood. We seek to understand how efficient quantum delegation schemes can be designed based on weaker or different complexity assumptions. We study how the availability of symmetric-key primitives, modeled by a random oracle, changes the complexity of quantum computation delegation. In contrast with public-key primitives, there are many candidates for symmetric-key schemes secure against quantum attacks. We aim for protocols that require as little quantum computing as possible for the client. Specifically, we ask that the client only needs to run a quantum circuit of size independent of the circuit being evaluated. Known unconditionally-secure protocols all require the client to evaluate quantum circuits of size at least linear in the original circuit size. In this thesis, we construct two new quantum computation delegation protocols. The first protocol is for the delegation of a large special circuit family, which we call "C+P circuits". This scheme is non-interactive, and can be used to delegate a very important quantum algorithm---Shor's algorithm (Shor,97) for integer factorization and discrete logarithms. Our second protocol requires interaction---one quantum message from the client to the server, and many rounds of classical computation---but supports arbitrary quantum computation (instead of a specific circuit family), and is thus much more general than the first protocol in both theory and practice. Both protocols are proved secure in the quantum random oracle model. The protocols can be instantiated in practice with a symmetric-key cipher such as AES.
Two of the fundamental no-go theorems of quantum information are the no-cloning theorem (that it is impossible to make copies of general quantum states) and the no-teleportation theorem (the prohibition on telegraphing, or sending quantum states over classical channels without pre-shared entanglement). They are known to be equivalent, in the sense that a collection of quantum states is telegraphable if and only if it is clonable. Our main result suggests that this is not the case when computational efficiency is considered. We give a collection of quantum states and quantum oracles relative to which these states are efficiently clonable but not efficiently telegraphable. Given that the opposite scenario is impossible (states that can be telegraphed can always trivially be cloned), this gives the most complete quantum oracle separation possible between these two important no-go properties. We additionally study the complexity class clonableQMA, a subset of QMA whose witnesses are efficiently clonable. As a consequence of our main result, we give a quantum oracle separation between clonableQMA and the class QCMA, whose witnesses are restricted to classical strings. We also propose a candidate oracle-free promise problem separating these classes. We finally demonstrate an application of clonable-but-not-telegraphable states to cryptography, by showing how such states can be used to protect against key exfiltration.
Semiquantum key distribution allows a quantum party to share a random key with a "classical" party who only can prepare and measure qubits in the computational basis or reorder some qubits when he has access to a quantum channel. In this work, we present a protocol where a secret key can be established between a quantum user and an almost classical user who only needs the quantum ability to access quantum channels, by securely delegating quantum computation to a quantum server. We show the proposed protocol is robust even when the delegated quantum server is a powerful adversary, and is experimentally feasible with current technology. As one party of our protocol is the most quantum-resource efficient, it can be more practical and significantly widen the applicability scope of quantum key distribution.
Unclonable cryptography is concerned with leveraging the no-cloning principle to build cryptographic primitives that are otherwise impossible to achieve classically. Understanding the feasibility of unclonable encryption, one of the key unclonable primitives, satisfying indistinguishability security in the plain model has been a major open question in the area. So far, the existing constructions of unclonable encryption are either in the quantum random oracle model or are based on new conjectures. We present a new approach to unclonable encryption via a reduction to a novel question about nonlocal quantum state discrimination: how well can non-communicating -- but entangled -- players distinguish between different distributions over quantum states? We call this task simultaneous state indistinguishability. Our main technical result is showing that the players cannot distinguish between each player receiving independently-chosen Haar random states versus all players receiving the same Haar random state. We leverage this result to present the first construction of unclonable encryption satisfying indistinguishability security, with quantum decryption keys, in the plain model. We also show other implications to single-decryptor encryption and leakage-resilient secret sharing.