论文标题
拓扑稳定器模型在有限温度下的纠缠成本
Entanglement cost in topological stabilizer models at finite temperature
论文作者
论文摘要
纠缠的概念对于表征物质量子阶段的普遍特性很有用。从量子信息理论的角度来看，很容易询问其纠缠结构是否具有任何操作含义，例如，通过自由操作（例如本地操作和经典交流（LOCC））来量化准备纠缠系统的成本。虽然答案对纯国肯定是肯定的，因为纠缠熵与纠缠成本相吻合，但混合国家的案例知之甚少。为此，我们研究了在积极的 - 特兰斯（PPT）保存操作下准备某些多体系统的热吉布斯所需的纠缠成本，这是一套包括LOCC的免费操作。具体来说，我们表明，对于$ d $ d $二维的圆环代码模型的$ d = 2、3、4 $，ppt纠缠成本完全等于纠缠的否定性，这是一种衡量混合状态纠缠的量度，该措施已知可以在有限温度下诊断拓扑顺序。
The notion of entanglement has been useful for characterizing universal properties of quantum phases of matter. From the perspective of quantum information theory, it is tempting to ask whether their entanglement structures possess any operational meanings, e.g., quantifying the cost of preparing an entangled system via free operations such as the local operations and classical communication (LOCC). While the answer is affirmative for pure states in that entanglement entropy coincides with entanglement cost, the case for mixed states is less understood. To this end, we study the entanglement cost required to prepare the thermal Gibbs states of certain many-body systems under positive-partial-transpose (PPT) preserving operations, a set of free operations that include LOCC. Specifically, we show that for the Gibbs states of $d$-dimensional toric code models for $d = 2, 3, 4$, the PPT entanglement cost exactly equals entanglement negativity, a measure of mixed-state entanglement that has been known to diagnose topological order at finite temperature.
