纠缠负性的模式矩阵微扰展开
Perturbative expansion of entanglement negativity using patterned matrix calculus
摘要：
负性是一种纠缠单调性，常用来量化两体纠缠。由于负性是密度矩阵的非解析函数，物理学文献中使用的现有方法不足以计算其导数。为此，我们开发了复杂的模式矩阵演算技术，并使用它们根据密度算子的任意变化对负性进行微扰分析。其结果是一个易于实施的扩展，可以进行到所有订单。在此过程中，我们提供了出现在负性定义中的部分转置映射的方便表示。我们的方法非常适合于研究在广泛的物理系统中的纠缠的增长和衰减，包括在多体系统中的纠缠的一般线性增长，并具有广泛的相关性的量子态和可观的许多功能。
英文摘要：
Negativity is an entanglement monotone frequently used to quantify entanglement in bipartite states. Because negativity is a non-analytic function of a density matrix, existing methods used in the physics literature are insufficient to compute its derivatives. To this end we develop techniques in the calculus of complex, patterned matrices and use them to conduct a perturbative analysis of negativity in terms of arbitrary variations of the density operator. The result is an easy-to-implement expansion that can be carried out to all orders. On the way we provide convenient representations of the partial transposition map appearing in the definition of negativity. Our methods are well-suited to study the growth and decay of entanglement in a wide range of physical systems, including the generic linear growth of entanglement in many-body systems, and have broad relevance to many functions of quantum states and observables.
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