论文标题
光滑，可区分功能的量子叠加的纠缠特性
Entanglement Properties of Quantum Superpositions of Smooth, Differentiable Functions
论文作者
论文摘要
我们提供了对应于平滑，可区分，实价（SDR）单变量功能的量子叠加的纠缠分析。对于大型系统离散化，SDR函数被低级矩阵乘积状态可缩小。我们表明，这些功能的最大von-neumann二分球熵随系统大小而对数增长。这意味着大型系统的矩阵乘积状态（MP）中存在有效的低级别近似值。作为推论，我们显示了等级2 MPS的痕量距离近似精度为$ω（\ log n/n）$的上限，这意味着这些低级别近似值可以准确地扩展到大量子系统。
We present an entanglement analysis of quantum superpositions corresponding to smooth, differentiable, real-valued (SDR) univariate functions. SDR functions are shown to be scalably approximated by low-rank matrix product states, for large system discretizations. We show that the maximum von-Neumann bipartite entropy of these functions grows logarithmically with the system size. This implies that efficient low-rank approximations to these functions exist in a matrix product state (MPS) for large systems. As a corollary, we show an upper bound on trace-distance approximation accuracy for a rank-2 MPS as $Ω(\log N/N)$, implying that these low-rank approximations can scale accurately for large quantum systems.
