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首页> 外文期刊>Physical Review X >Energy as a Detector of Nonlocality of Many-Body Spin Systems
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Energy as a Detector of Nonlocality of Many-Body Spin Systems

机译：能量作为多体自旋系统非局部性的检测器

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We present a method to show that low-energy states of quantum many-body interacting systems in one spatial dimension are nonlocal. We assign a Bell inequality to the Hamiltonian of the system in a natural way and we efficiently find its classical bound using dynamic programing. The Bell inequality is such that its quantum value for a given state, and for appropriate observables, corresponds to the energy of the state. Thus, the presence of nonlocal correlations can be certified for states of low enough energy. The method can also be used to optimize certain Bell inequalities: in the translationally invariant (TI) case, we provide an exponentially faster computation of the classical bound and analytically closed expressions of the quantum value for appropriate observables and Hamiltonians. The power and generality of our method is illustrated through four representative examples: a tight TI inequality for eight parties, a quasi-TI uniparametric inequality for any even number of parties, ground states of spin-glass systems, and a nonintegrable interacting X X Z -like Hamiltonian. Our work opens the possibility for the use of low-energy states of commonly studied Hamiltonians as multipartite resources for quantum information protocols that require nonlocality.
机译：我们提出一种方法来证明一个空间维度上的量子多体相互作用系统的低能态是非局部的。我们以自然的方式将Bell不等式分配给系统的哈密顿量，并使用动态编程有效地找到其经典界限。贝尔不等式使得对于给定状态以及适当的可观测量，其量子值与该状态的能量相对应。因此，对于能量足够低的状态，可以证明存在非局部相关性。该方法还可以用于优化某些Bell不等式：在平移不变（TI）的情况下，对于适当的可观测量和哈密顿量，我们提供了量子值的经典有界和解析式闭合表达式的指数级更快计算。通过四个有代表性的示例来说明我们方法的能力和一般性：八个方的紧密TI不等式，任何偶数方的准TI单参数不等式，自旋玻璃系统的基态以及不可积分的类似XXZ的相互作用哈密​​尔顿我们的工作为将通常研究的哈密顿量的低能态用作需要非局域性的量子信息协议的多方资源开辟了可能性。

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