统一量子no-go定理与限制集上量子态的变换
Unified quantum no-go theorems and transforming of quantum states in a restricted set
摘要：
量子力学中的线性叠加原理是不可克隆定理、不可删除定理和不可叠加定理等几个不可通过定理的基础。找到一般的禁止原则来统一这些结果仍然是一个悬而未决的问题。在本文中，我们研究一般的量子变换禁止或允许的叠加原理为各种目标。首先，我们证明了一个无编码定理，该定理禁止了有限维希尔伯特空间中未知纯态和固定态的线性叠加。两种一般形式包括作为特例的不可克隆定理、不可删除定理和不可叠加定理。其次，我们提供了一个统一的方案，以一次性的方式呈现完美和不完美的量子任务（克隆和删除）。该方案可以产生富有成效的结果，其完全特征在于输入纯态的线性无关性。成功概率的广义上界将被证明。第三，我们推广了最近的叠加未知的状态与固定的重叠时，多个副本的输入状态。
英文摘要：
The linear superposition principle in quantum mechanics is essential for several no-go theorems such as the no-cloning theorem, the no-deleting theorem and the no-superposing theorem. It remains an open problem of finding general forbidden principles to unify these results. In this paper, we investigate general quantum transformations forbidden or permitted by the superposition principle for various goals. First, we prove a no-encoding theorem that forbids linearly superposing of an unknown pure state and a fixed state in Hilbert space of finite dimension. Two general forms include the no-cloning theorem, the no-deleting theorem, and the no-superposing theorem as special cases. Second, we provide a unified scheme for presenting perfect and imperfect quantum tasks (cloning and deleting) in a one-shot manner. This scheme may yield to fruitful results that are completely characterized with the linear independence of the input pure states. The generalized upper bounds for the success probability will be proved. Third, we generalize a recent superposing of unknown states with fixed overlaps when multiple copies of the input states are available.
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