Unconditional efficient one-bit unclonable encryption
The answer is affirmative. For every , there exists a one-time private-key quantum encryption scheme for one-bit classical messages with a -bit classical key and an -qubit ciphertext. The scheme has perfect correctness, efficient encryption and decryption using only single-qubit Clifford gates and local Pauli measurements, and is information-theoretically unclonable-indistinguishable: against every information-theoretic pre-key-splitting attack, the probability of winning the one-bit unclonable-indistinguishability experiment is at most . Thus the adversarial advantage is exponentially small in .
Progress summary
The requested scheme has been constructed and published on arXiv, with perfect correctness and an attack advantage that shrinks exponentially.
The problem asks for an efficient, plain-model, information-theoretically secure one-time scheme encrypting one classical bit. Botteron et al. are credited with first conceiving the underlying construction.
Known results
- Earlier work established an unconditional unclonable bit, but the retrieved source does not establish all the requested efficiency and plain-model properties.
- Botteron et al. (2026) obtained classical-key security; subsequent work improved the efficiency and security tradeoffs.
July 2026 efficient construction
Two arXiv papers report the requested result. The construction uses a -bit key and an -qubit ciphertext, with efficient single-qubit Clifford encryption, local Pauli-measurement decryption, and perfect correctness. Its winning probability is at most , so the adversarial advantage is exponentially small. One paper states that its construction and main proof ideas were generated by GPT 5.6 Sol Ultra.
Current status (as of July 2026): The problem is resolved by arXiv constructions with efficient algorithms, information-theoretic security, and advantage at most ; no substantive part of the stated goal remains open.
Solutions 0
No solutions have been posted yet.