论文标题
通过$ q $分布来检测相空间中的连续变量纠缠
Detecting continuous variable entanglement in phase space with the $Q$-distribution
论文作者
论文摘要
我们证明了基于Husimi $ Q $分布的一般连续变量纠缠标准，该标准通过使用Lieb and Solovej采用定理来代表规范相空间中的量子状态。我们讨论了它们的普遍性，从连续的多数化理论的角度来看，这有可能优化一组凹功能的功能，并表明，这种方法属于熵和第二刻的标准，也遵循特殊情况。将所有派生的标准与相应的基于边缘的标准进行比较，并且在只有我们的标准标志纠缠的原型示例家族中，证明了相空间方法的强度。此外，我们在两个具有稀疏数据的实验相关场景中探索了他们的优化前景：有限的检测器分辨率和有限的统计数据。在这两种情况下，优化都可以明确改善检测状态类别和检测的信噪比。
We prove a general class of continuous variable entanglement criteria based on the Husimi $Q$-distribution, which represents a quantum state in canonical phase space, by employing a theorem by Lieb and Solovej. We discuss their generality, which roots in the possibility to optimize over the set of concave functions, from the perspective of continuous majorization theory and show that with this approach families of entropic as well as second moment criteria follow as special cases. All derived criteria are compared to corresponding marginal based criteria and the strength of the phase space approach is demonstrated for a family of prototypical example states where only our criteria flag entanglement. Further, we explore their optimization prospects in two experimentally relevant scenarios characterized by sparse data: finite detector resolution and finite statistics. In both scenarios optimization leads to clear improvements enlarging the class of detected states and the signal-to-noise ratio of the detection, respectively.
