AI 中文总结
研究针对单个经典比特的加密方案，提出基于泡利本征态的方法，构建了明文模型、信息理论安全且高效的不可克隆加密方案，可实现多次安全的$1 \to 2$加密，具有指数安全性，给出了最佳概率界限。
AI 中文摘要
据我们所知，我们给出了首个针对单个经典比特的明文模型、一次性信息理论安全且高效的不可克隆加密方案。之前Bhattacharyya和Culf（《自然物理学》，2026年）以及Bhattacharyya、Broadbent和Culf的工作要么仅显示出$1/\mathsf{poly}(\lambda)$的安全损失，要么需要低效的加密/解密操作。我们避免了这两个问题，在此过程中，假设存在类似伪随机函数的状态（Bartusek和Goldin），我们获得了首个针对任意多项式长度消息的多次安全的$1 \to 2$不可克隆加密的明文模型构造。密钥是$n$个量子比特上的均匀随机非恒等同相无泡利算符，比特$a$被加密为该泡利算符的随机$(-1)^a$本征态。该方案具有指数安全性，我们证明两个接收者都恢复该比特的概率至多为$\frac{1}{2}+\frac{1}{2}\sqrt{{2^n}/({4^n - 1})} = \frac{1}{2} + O\left(2^{-n/2}\right)$。根据Broadbent、Culf和Rochette的下限，这是使用$n$量子比特密文可实现的最佳概率界限（直至$O(\cdot)$中隐藏的常数）。主要概念思想是在精确的谱意义上利用泡利群的平衡对易 - 反对易结构。证明虽然复杂但完全是基础的，并使用了标准的谱界技术。主要技术工具是一个独立的线性代数引理，它非正式地关联了两个不同算符的正定性，每个算符都体现了如果两个接收者能够频繁地单独解密，那么他们也必然经常产生分歧的直觉。GPT - 5.6 Sol Ultra在与作者的扩展对话中找到了这个证明并起草了本文的初稿。作者对本文的正确性负全部责任。
英文摘要
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 $1/\mathsf{poly}(λ)$ 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 $1 \to 2$ 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 $\frac{1}{2}+\frac{1}{2}\sqrt{{2^n}/({4^n-1})} = \frac{1}{2} + O\left(2^{-n/2}\right).$ 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 $O(\cdot)$). 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.
