全局纠缠量化：基于经典阴影技术
Global Entanglement Quantification via Classical Shadows
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中文总结 AI 辅助
本文提出利用经典阴影技术高效量化多体纠缠度量$E_G^{(n)}$，通过估计线性熵减少测量次数，模拟表明该方法优于直接估计，无需重建密度算子。
中文摘要 AI 辅助
检测和表征量子关联是量子信息中具有高度相关性的任务。更具体地说，量化多体纠缠的程度是一项公认的困难任务，即使对于纯态也是如此。为此，人们已经提出了多种纠缠度量，但目前尚无通用的方法。在这项工作中，我们提出使用经典阴影技术来测量在Phys. Rev. A 74, 022314中引入的广义全局纠缠。这一特定的多体纠缠量化器$E_G^{(n)}$依赖于一个状态的所有$n$量子比特划分的线性熵。由于线性熵可以用子系统的完备可观测量集合来表示，我们采用经典阴影来以较少的测量次数估计许多可观测量。我们模拟了对已知纠缠态和随机态的$E_G^{(n)}$量化，比较了阴影估计和分组技术。我们的结果显示了经典阴影相对于直接估计方法的明显优势，表明它可以作为一种有用的工具来量化纠缠，而无需重建整个系统的密度算子。
英文摘要
Detecting and characterizing quantum correlations are tasks of great relevance in quantum information. More specifically, quantifying the amount of multipartite entanglement is a known difficult task, even for pure states. To this end, several entanglement measures have been proposed, although there is currently no universal manner to do so. In this work, we propose the classical shadows technique to measure the generalized global entanglement introduced in Phys. Rev. A 74, 022314. This particular multipartite entanglement quantifier $E_G^{(n)}$ relies on the linear entropies of all $n$-qubit partitions of a state. As the linear entropy can be written in terms of a complete set of observables of the subsystem, we employ classical shadows to estimate many observables with fewer measurements. We simulate the quantification of $E_G^{(n)}$ for well-known entangled states and for random states, comparing shadow estimations and grouping techniques. Our results show a clear advantage of classical shadows over direct estimation approaches, indicating that it can be a useful tool to quantify entanglement without the need to reconstruct the density operator of the whole system.
发表机构
- Universidade Federal de Santa Catarina（圣卡塔琳娜联邦大学）
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