We show the following unconditional results on quantum commitments in two related yet different models: 1. We revisit the notion of quantum auxiliary-input commitments introduced by Chailloux, Kerenidis, and Rosgen (Comput. Complex. 2016) where both the committer and receiver take the same quantum state, which is determined by the security parameter, as quantum auxiliary inputs. We show that computationally-hiding and statistically-binding quantum auxiliary-input commitments exist unconditionally, i.e., without relying on any unproven assumption, while Chailloux et al. assumed a complexity-theoretic assumption, ${\bf QIP}\not\subseteq{\bf QMA}$. On the other hand, we observe that achieving both statistical hiding and statistical binding at the same time is impossible even in the quantum auxiliary-input setting. To the best of our knowledge, this is the first example of unconditionally proving computational security of any form of (classical or quantum) commitments for which statistical security is impossible. As intermediate steps toward our construction, we introduce and unconditionally construct post-quantum sparse pseudorandom distributions and quantum auxiliary-input EFI pairs which may be of independent interest. 2. We introduce a new model which we call the common reference quantum state (CRQS) model where both the committer and receiver take the same quantum state that is randomly sampled by an efficient setup algorithm. We unconditionally prove that there exist statistically hiding and statistically binding commitments in the CRQS model, circumventing the impossibility in the plain model. We also discuss their applications to zero-knowledge proofs, oblivious transfers, and multi-party computations.

翻译：我们展示了在两种相关但不同的模型下关于量子承诺的以下无条件结果：1. 重新审视由Chailloux、Kerenidis和Rosgen（Comput. Complex. 2016）引入的量子辅助输入承诺概念，其中承诺者和接收者均接收由安全参数决定的相同量子态作为量子辅助输入。我们证明，计算隐藏且统计绑定的量子辅助输入承诺无条件存在，即不依赖任何未证假设，而Chailloux等人曾依赖复杂度理论假设${\bf QIP}\not\subseteq{\bf QMA}$。另一方面，我们观察到即使在量子辅助输入设置中，同时实现统计隐藏和统计绑定也是不可能的。据我们所知，这是首个无条件证明统计安全性不可行的（经典或量子）承诺具有计算安全性的实例。作为构建的中间步骤，我们引入并无条件构建了后量子稀疏伪随机分布和量子辅助输入EFI对，这些结果可能具有独立研究价值。2. 我们引入一种新模型，称为公共参考量子态（CRQS）模型，其中承诺者和接收者均接收由高效设置算法随机采样的相同量子态。我们无条件证明在CRQS模型中存在统计隐藏且统计绑定的承诺，从而规避了朴素模型中的不可能性。我们还讨论了其在零知识证明、不经意传输和安全多方计算中的应用。