Unconditional uncloneable encryption of a single bit with efficient encryption and decryption is now possible. However, whether the extension to messages of arbitrary length achieves statistical security remains to be known. Using the fact that the encoding bases for the single-bit scheme known to be secure consist of a subset of the Clifford unitaries, we show that this scheme can be upgraded to achieve unconditional uncloneable encryption for messages of arbitrary length, with encoding time polynomial in the message length and security parameter. This establishes that one-time uncloneable encryption of arbitrary messages enjoys statistical security.
Unconditional uncloneable encryption of a single bit with efficient encryption and decryption is now possible. However, whether the extension to messages of arbitrary length achieves statistical security remains to be known. Using the fact that the encoding bases for the single-bit scheme known to be secure consist of a subset of the Clifford unitaries, we show that this scheme can be upgraded to achieve unconditional uncloneable encryption for messages of arbitrary length, with encoding time polynomial in the message length and security parameter. This establishes that one-time uncloneable encryption of arbitrary messages enjoys statistical security.
In this note, we consider the setting of uncloneable encryption satisfying uncloneable indistinguishability, a form of symmetric key encryption that prevents the cloning of ciphertexts in a very strong sense. Our goal is to minimize the assumptions under which (many-time secure) uncloneable encryption is known to exist, assuming the existence of an information-theoretic "uncloneable bit", i.e. a one-time secure uncloneable encryption scheme for one-bit messages. We observe that if a t -> t' uncloneable bit exists, then the following implications hold.
1. If many-time secure symmetric key encryption exists, then many-time secure t -> t' uncloneable encryption for arbitrary-length messages exists. Since many-time secure uncloneable encryption implies many-time secure symmetric key encryption, this result is tight.
2. If pseudorandom unitaries exist, then many-time secure t -> t' uncloneable encryption for arbitrary-length messages with identical copy security exists.
These results together show that many-time secure uncloneable encryption may follow from concrete assumptions in "microcrypt", the world of unstructured quantum cryptography that plausibly exists even if P = NP.
We give an unconditional construction of information-theoretically secure one-time private-key unclonable encryption for one-bit messages, with efficient encryption and decryption and exponentially small unclonable-indistinguishability advantage. Previous work by Bhattacharyya and Culf (Nature Physics, 2026) and Bhattacharyya, Broadbent, and Culf (arXiv:2603.08916) either only showed inverse-polynomial security loss or required inefficient encryption/decryption operations; we avoid both of these caveats.
Our scheme's key is a uniformly random non-identity phase-free Pauli on n qubits, and bit a is encrypted as a random (−1)a eigenstate of that Pauli. We prove that the probability that both receivers recover the bit is at most 1/2+O(2−n/2). By a lower bound due to Broadbent, Culf, and Rochette (arXiv:2510.00903), this is the best probability bound achievable with n-qubit ciphertexts while ensuring perfect correctness (up to the constant hidden in the O(⋅)).
We give, to our knowledge, the first plain-model, one-time information-theoretically secure, efficient unclonable encryption scheme for one classical bit. Previous work by Bhattacharyya and Culf (Nature Physics, 2026) and Bhattacharyya, Broadbent, and Culf either only showed 1/poly(λ) security loss or required inefficient encryption/decryption operations. We avoid both of these caveats; in doing so, we obtain (to our knowledge) the first plain-model construction of many-time secure 1→2 unclonable encryption for arbitrary polynomial-length messages, assuming the existence of pseudorandom function-like states (Bartusek and Goldin).
The key is a uniformly random non-identity phase-free Pauli on n qubits, and bit a is encrypted as a random (−1)a eigenstate of that Pauli. The scheme is exponentially secure; we prove that the probability that both receivers recover the bit is at most 21+212n/(4n−1)=21+O(2−n/2). By a lower bound due to Broadbent, Culf, and Rochette, this is the best probability bound achievable with n-qubit ciphertexts (up to the constant hidden in the O(⋅)).
The main conceptual idea is to leverage, in a precise spectral sense, the balanced commutation-anticommutation structure of the Pauli group. The proof is intricate but completely elementary and makes use of standard spectral bound techniques. The main technical workhorse is a standalone linear-algebraic lemma that informally relates the positivity of two different operators, each capturing the intuition that if the two receivers can individually decrypt unusually often then they must also disagree often.
GPT-5.6 Sol Ultra found this proof in an extended conversation with the author and drafted a preliminary version of this paper. The author is fully accountable for the correctness of this paper.
We establish quantum uncloneable encryption with unconditional security, preventing two non-communicating adversaries from simultaneously decrypting a single ciphertext − even when both are given the key. Our construction achieves security that approaches the ideal limit at a rate that is exponentially small in the security parameter, without employing any assumptions. Our proof invokes unitary invariance of the shared entangled state and simplifies the adversarial strategies by enforcing this symmetry. Crucially, it then rules out the sender being highly correlated with two non-communicating adversaries at once by an approximation property that we develop, for such unitarily invariant states, which yields a near-optimal bound on the probability of cloning. Consequently, no coordinated strategy beats random guessing of the encrypted bit, establishing unconditional uncloneability. This reveals the existence of an uncloneable bit in Nature and delineates a fundamental, physically enforced cryptographic primitive unavailable in classical settings.
Uncloneable encryption is a cryptographic primitive which encrypts a classical message into a quantum ciphertext, such that two quantum adversaries are limited in their capacity of being able to simultaneously decrypt, given the key and quantum side-information produced from the ciphertext. Since its initial proposal and scheme in the random oracle model by Broadbent and Lord [TQC 2020], uncloneable encryption has developed into an important primitive at the foundation of quantum uncloneability for cryptographic primitives. Despite sustained efforts, however, the question of unconditional uncloneable encryption (and in particular of the simplest case, called an uncloneable bit) has remained elusive. Here, we propose a candidate for the unconditional uncloneable bit problem, and provide strong evidence that the adversary's success probability in the related security game converges quadratically as 1 / 2 + 1 / ( 2 K ) , where K represents the number of keys and 1 / 2 is trivially achievable. We prove this bound's validity for K ranging from 2 to 7 and demonstrate the validity up to K = 17 using computations based on the NPA hierarchy. We furthemore provide compelling heuristic evidence towards the general case. In addition, we prove an asymptotic upper bound of 5 / 8 and give a numerical upper bound of ∼ 0.5980 , which to our knowledge is the best-known value in the unconditional model.
Quantum states cannot be cloned. I show how to extend this property to classical messages encoded using quantum states, a task I call ``uncloneable encryption.'' An uncloneable encryption scheme has the property that an eavesdropper Eve not only cannot read the encrypted message, but she cannot copy it down for later decoding. She could steal it, but then the receiver Bob would not receive the message, and would thus be alerted that something was amiss. I prove that any authentication scheme for quantum states acts as a secure uncloneable encryption scheme. Uncloneable encryption is also closely related to quantum key distribution (QKD), demonstrating a close connection between cryptographic tasks for quantum states and for classical messages. Thus, studying uncloneable encryption and quantum authentication allows for some modest improvements in QKD protocols. While the main results apply to a one-time key with unconditional security, I also show uncloneable encryption remains secure with a pseudorandom key. In this case, to defeat the scheme, Eve must break the computational assumption behind the pseudorandom sequence before Bob receives the message, or her opportunity is lost. This means uncloneable encryption can be used in a non-interactive setting, where QKD is not available, allowing Alice and Bob to convert a temporary computational assumption into a permanently secure message.