Pauli encodings for unclonable encryption

The problem asks whether an efficient one-bit quantum encryption scheme can stop an adversary from producing two ciphertext systems that both reveal the plaintext once the key is disclosed. The 2026 work studies this question for encryption based on Pauli eigenspace projectors, rather than all possible schemes.

Known results

• Every Pauli Encoding using $K$ keys has optimal monogamy-of-entanglement winning probability at least $\frac{1}{2}+\frac{1}{2\sqrt{K}}$.
• Restricting keys to Pauli strings of only $X$ and $Z$ is insecure.
• The BB84 family has winning probability $\cos^2(\pi/8)=\frac{1}{2}+\frac{1}{2\sqrt{2}}$ and fails weak unclonable-indistinguishability security.
• For pairwise anticommuting Pauli strings, a third-level semidefinite-programming bound is asymptotically about $0.5556$; matching optimality remains conjectural.

July 2026 efficient construction

An accompanying paper claims an efficient, information-theoretically secure one-time scheme based on random Pauli eigenstates, with both-recipient recovery probability at most $\frac{1}{2}+\frac{1}{2}\sqrt{\frac{2^n}{4^n-1}}=\frac{1}{2}+O(2^{-n/2})$. It also claims a many-time extension under a pseudorandom-state assumption.

Current status (as of July 2026): Pauli-based constructions have substantial positive and negative results, including a claimed efficient scheme, but no source establishes the assertion for all efficient one-bit quantum encryption schemes.