一般矩阵乘积态的经典限制是准局部吉布斯的
Classical restrictions of generic matrix product states are quasi-locally Gibbsian
摘要：
我们证明了一维格点上有限量子系统关于局部标准正交基（经典限制）的范数平方振幅可以用局部哈密顿量的吉布斯态指数地很好地近似（即，是准局部吉布斯），如果经典的条件互信息（CMI）的任何连接的三分格是迅速衰减的宽度的中间区域。对于内射矩阵产品状态，我们还表明，经典的CMI指数衰减，每当矩阵产品运营商的集合满足“纯度条件”，以前建立的随机矩阵产品理论的概念。此外，我们表明，违反纯度条件，使一个广义的概念，错误校正的虚拟空间，从而表明这种违反的非通用性质。我们通过构建一个概率模型使这种直觉更加具体，其中纯度是一个典型的属性。我们的主要结果的证明广泛地利用了随机矩阵乘积的理论，并可能在其他地方找到应用。
英文摘要：
We show that the norm squared amplitudes with respect to a local orthonormal basis (the classical restriction) of finite quantum systems on one-dimensional lattices can be exponentially well approximated by Gibbs states of local Hamiltonians (i.e., are quasi-locally Gibbsian) if the classical conditional mutual information (CMI) of any connected tripartition of the lattice is rapidly decaying in the width of the middle region. For injective matrix product states, we moreover show that the classical CMI decays exponentially, whenever the collection of matrix product operators satisfies a 'purity condition'; a notion previously established in the theory of random matrix products. We furthermore show that violations of the purity condition enables a generalized notion of error correction on the virtual space, thus indicating the non-generic nature of such violations. We make this intuition more concrete by constructing a probabilistic model where purity is a typical property. The proof of our main result makes extensive use of the theory of random matrix products, and may find applications elsewhere.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
