论文标题
部分可观测时空混沌系统的无模型预测
Randomized channel-state duality
论文作者
论文摘要
频道状态二元性是量子信息科学的核心结果。它指的是动态过程（量子通道）和放大的希尔伯特空间中的静态量子状态之间的对应关系。由于通常混合了相应的双重状态，因此由遗传学矩阵描述。在本文中，我们提出了一个随机的频道状态双重性。换句话说，量子通道由从随机源产生的$ n $纯量子状态的集合表示。关于适当的距离度量，这种随机二元关系的准确性由$ 1/n $给出。对于大型系统，$ n $比量子通道的确切双基质的尺寸小得多。这提供了任何量子通道的高度准确的低级别近似值，并且由于二元性关系，这是混合量子状态的有效数据压缩方案。我们证明了随机通道状态双重性的这两个即时应用，具有混乱的$ 1 $维自旋系统。
Channel-state duality is a central result in quantum information science. It refers to the correspondence between a dynamical process (quantum channel) and a static quantum state in an enlarged Hilbert space. Since the corresponding dual state is generally mixed, it is described by a Hermitian matrix. In this article, we present a randomized channel-state duality. In other words, a quantum channel is represented by a collection of $N$ pure quantum states that are produced from a random source. The accuracy of this randomized duality relation is given by $1/N$, with regard to an appropriate distance measure. For large systems, $N$ is much smaller than the dimension of the exact dual matrix of the quantum channel. This provides a highly accurate low-rank approximation of any quantum channel, and, as a consequence of the duality relation, an efficient data compression scheme for mixed quantum states. We demonstrate these two immediate applications of the randomized channel-state duality with a chaotic $1$-dimensional spin system.
