The use of the mutual information (MI) as a measure of the entanglement in quantum systems has gained a consensus in recent years, even if there is an ongoing effort to distinguish the classical and quantum contributions contained therein. This quantity has been first introduced in condensed matter physics, in particular, in studies based on the density matrix renormalization group method. This method has been successfully adapted to quantum chemistry problems, opening the way to compute MI also in molecular systems. A key aspect of this quantity is its dependence on the one-electron (orbital) basis set, even for wave functions that are invariant under unitary transformation of the orbitals. In this work, we investigate the role of the orbital basis set (delocalized or localized, following different strategies) for wave functions expressed as linear combinations of Slater determinants and we give the analytic expression for the MI for a few special cases. This study aims to improve the knowledge of the relationship between the characteristics of the chemical bond (considering a few paradigmatic molecules, H2, F2, N2, and short linear polyenes) and the properties of interest in the field of quantum information theory.

中文翻译：

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分子中的纠缠和互信息：比较局部和离域轨道。


近年来，使用互信息 （MI） 作为量子系统纠缠的度量已经达成共识，即使人们一直在努力区分其中包含的经典贡献和量子贡献。这个量首先被引入凝聚态物理学中，特别是在基于密度矩阵重整化群方法的研究中。这种方法已成功应用于量子化学问题，为在分子系统中计算 MI 开辟了道路。这个量的一个关键方面是它对单电子（轨道）基集的依赖性，即使对于在轨道的幺正变换下不变的波函数也是如此。在这项工作中，我们研究了轨道基集（离域或局部化，遵循不同的策略）对表示为 Slater 行列式线性组合的波函数的作用，并给出了一些特殊情况下 MI 的解析表达式。本研究旨在提高对化学键特性（考虑一些范式分子、H2、F2、N2 和短线性多烯）与量子信息论领域感兴趣的性质之间关系的认识。