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arXiv 2407.04058quant-phcond-mat.stat-mech
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通过热力学功提取测量多体量子关联

Measuring multipartite quantum correlations by thermodynamic work extraction

The University of Tokyo(东京大学);RIKEN Cluster for Pioneering Research (CPR)(理化学研究所先导研究集群);JST, PRESTO(日本科学技术振兴机构,PRESTO项目)

Toshihiro Yada, Nobuyuki Yoshioka, Takahiro Sagawa

AI总结:

本文提出基于热力学功提取的多体量子关联度量,通过高效方法计算并验证其在量子多体系统中的应用。

摘要:

量子关联是量子力学的核心,对各种领域起着关键作用。尽管双体量子关联已被广泛研究,但在多体系统中多体量子关联仍然难以捉摸,因为其结构复杂。特别是,计算多体量子关联度量往往需要指数级成本。在本文中,我们通过热力学方法解决这个问题;我们引入了一种基于全局操作和本地操作与经典通信(LOCC)所提取的热力学功差异的多体量子关联度量。这可以被视为工作亏缺的多体推广,后者已被关注作为双体量子关联的热力学度量。热力学方法处理多体量子关联的一个显著特点是,我们可以用有明确操作意义的方式比较量子关联的程度。重要的是,我们开发了一种高效的计算多体工作亏缺的方法。这种方法适用于由矩阵乘积态(MPS)描述的特殊类量子多体系统,其中数值成本被证明与系统大小成正比,显著降低了直接计算所需的指数成本。我们在AKLT态和簇态中演示了这种方法,并解析地获得了该度量的精确值。我们进一步表明,由MPS描述的量子相变很好地由多体工作亏缺捕捉。这表明,多体工作亏缺不仅突显了多体量子关联与量子热力学之间的基本联系,而且也作为高效计算量子多体系统结构的探针。

英文摘要:

Quantum correlations are at the core of quantum mechanics and play a crucial role in various fields. While bipartite quantum correlations have been extensively studied, multipartite quantum correlations in many-body systems remain elusive due to their complex structure. In particular, a primary challenge lies in the fact that the calculation of multipartite quantum correlation measure often requires exponential cost. In this work, we tackle this problem by adopting a thermodynamic approach; we introduce a measure of multipartite quantum correlations based on the difference in extractable thermodynamic work by global operations and local operations and classical communication (LOCC). This can be regarded as a multipartite generalization of the work deficit, which has attracted attention as a thermodynamic measure of bipartite quantum correlation. A distinguishing feature of the thermodynamic approach to multipartite quantum correlation is that we can compare the degree of quantum correlations with clear operational meaning. Importantly, we develop an efficient calculation method of the multipartite work deficit. This efficient method works for a special class of quantum many-body systems described by matrix product states (MPS), where the numerical cost is shown to be proportional to the system size, significantly reducing the exponential cost required for the direct calculations. We demonstrate this efficient method in the AKLT state and the cluster state, and analytically obtain the exact values of this measure. We further show that a quantum phase transition described by MPS is well captured by the multipartite work deficit. This shows that the multipartite work deficit does not only highlight the fundamental connection between multipartite quantum correlations and quantum thermodynamics, but also serves as an efficiently-computable probe of the structures of quantum many-body systems.

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。

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