论文标题
在复杂和真实的量子力学中隐藏和掩盖量子信息
Hiding and masking quantum information in complex and real quantum mechanics
论文作者
论文摘要
经典信息可以完全隐藏在两分量子系统的相关性中。但是，根据最近得出的无隐藏和掩盖定理，不可能隐藏或掩盖所有量子信息。在这里，我们表明，任何一组信息完整的量子状态都不可隐藏，也不可掩盖，从而增强了以前已知的无内隐和掩盖定理。然后，借助Hurwitz-Radon矩阵（Clifford代数的表示），我们表明，关于实际量子状态的信息可以完全隐藏在相关性中，尽管所需的复合希尔伯特空间的最小维度会随着原始希尔伯特空间的维度而成倍增加。此外，一组实际量子状态是量子理论中最大掩盖的集合，与最大纠缠状态具有令人惊讶的联系。这些结果为隐藏和掩盖量子信息的潜在和极限提供了宝贵的见解，这些信息对许多活跃的研究领域具有内在兴趣。
Classical information can be completely hidden in the correlations of bipartite quantum systems. However, it is impossible to hide or mask all quantum information according to the no-hiding and no-masking theorems derived recently. Here we show that any set of informationally complete quantum states is neither hidable nor maskable, thereby strengthening the no-hiding and no-masking theorems known before. Then, by virtue of Hurwitz-Radon matrices (representations of the Clifford algebra), we show that information about real quantum states can be completely hidden in the correlations, although the minimum dimension of the composite Hilbert space required increases exponentially with the dimension of the original Hilbert space. Moreover, the set of real quantum states is a maximal maskable set within quantum theory and has a surprising connection with maximally entangled states. These results offer valuable insight on the potential and limit of hiding and masking quantum information, which are of intrinsic interest to a number of active research areas.
