论文标题
通用矩阵产品状态的经典限制是准局部吉布斯式的
Classical restrictions of generic matrix product states are quasi-locally Gibbsian
论文作者
论文摘要
我们表明，相对于当地量子系统对一维晶格的局部正交基础（经典限制）的规范平方的幅度可以被指数近似于吉布斯州的吉布斯州的吉布斯州（即准利的gibbsian cmi cmi cmi cmi cmi contice in Contriely Inception in Comi of Comi in Connation）的吉布斯（Gibbs）状态（即，cmi clastical gibbsian）均可吻合。中部地区的宽度。对于Injective矩阵产品状态，我们还表明，每当矩阵产品运营商满足“纯度条件”时，经典的CMI呈指数衰减；先前在随机基质产物理论中建立的概念。我们进一步表明，违反纯度条件的行为可以在虚拟空间上进行通用的误差校正概念，从而表明了这种违规的非传统性质。我们通过构建纯度是典型属性的概率模型来使这种直觉更具体。我们主要结果的证明是广泛使用随机矩阵产品的理论，并可能在其他地方找到应用。
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.
