论文标题
使用局部相关矩阵零的边界纠缠熵
Bounding Entanglement Entropy Using Zeros of Local Correlation Matrices
论文作者
论文摘要
相关函数和纠缠是表征量子多体态的两个不同方面。尽管许多相关函数在实验上都是可以访问的，但纠缠熵（EE）通常很难测量量子纠缠的最简单表征。在这封信中，我们提出了一项协议，以通过本地测量来绑定EE。该协议利用局部相关矩阵，并专注于其（近似）零特征值。给定量子状态，每个（近似）零特征值可用于定义一组局部投影算子。然后，可以通过概括这些投影仪来构建辅助哈密顿辅助。当构造仅涉及零特征值的投影仪时，我们证明了子系统的EE受到该子系统上辅助汉密尔顿的基础变性的限制。当包括非零特征值的投影仪时，我们表明EE可以通过子系统的热熵界定。我们的方案可以实验应用以研究在量子模拟器中制备的外来量子多体态。
Correlation functions and entanglement are two different aspects to characterize quantum many-body states. While many correlation functions are experimentally accessible, entanglement entropy (EE), the simplest characterization of quantum entanglement, is usually difficult to measure. In this Letter, we propose a protocol to bound EE by local measurements. This protocol utilizes local correlation matrices and focuses on their (approximate) zero eigenvalues. Given a quantum state, each (approximate) zero eigenvalue can be used to define a set of local projection operators. An auxiliary Hamiltonian can then be constructed by summing these projectors. When the construction only involves projectors of zero eigenvalues, we prove the EE of a subsystem is bounded by the ground-state degeneracy of the auxiliary Hamiltonian on this subsystem. When projectors from nonzero eigenvalues are included, we show the EE can be bounded by a thermal entropy of the subsystem. Our protocol can be applied experimentally to investigate exotic quantum many-body states prepared in quantum simulators.
