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Quantum and Classical Correlations in the Solid-State NMR Free Induction Decay

机译:固态NMR自由感应衰变中的量子和经典相关性

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The free induction decay (FID) of the transverse magnetization in a dipolar-coupled rigid lattice is a fundamental problem in magnetic resonance and in the theory of many-body systems. As it was shown earlier the FID shapes for the systems of classical magnetic moments and for quantum nuclear spin ones coincide if there are many nearly equivalent nearest neighbors n in a solid lattice. In this paper, we reduce a multispin density matrix of above system to a two-spin matrix. Then we obtain analytic expressions for the mutual information and the quantum and classical parts of correlations at the arbitrary spin quantum number S, in the high-temperature approximation. The time dependence of these functions is expressed via the derivative of the FID shape. To extract classical correlations for S>1/2 we provide generalized POVM measurement (positive-operator-valued measure) using the basis of spin coherent states. We show that in every pair of spins the portion of quantum correlations changes from 1/2 to 1/(S + 1) when S is growing up, and quantum properties disappear completely only if S → ∞.
机译:在偶极耦合的刚性晶格中,横向磁化的自由感应衰减(FID)是磁共振和多体系统理论中的一个基本问题。如前所述,如果在固体晶格中有许多几乎相等的最近邻,则经典磁矩系统和量子核自旋系统的FID形状会重合。在本文中,我们将上述系统的多轴密度矩阵简化为两轴矩阵。然后,在高温近似下,获得了互信息以及任意自旋量子数S下相关性的量子和经典部分的解析表达式。这些功能的时间依赖性通过FID形状的导数表示。为了提取S> 1/2的经典相关性,我们使用自旋相干态的基础提供了广义的POVM测量(正算值)。我们表明,在每对自旋中,当S长大时,量子相关性的部分从1/2变为1 /(S +1),仅当S→∞时,量子性质才会完全消失。

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