We discuss recent developments in measurement protocols that generate quantum entanglement between two remote qubits, focusing on the theory of joint continuous detection of their spontaneous emission. We consider a device geometry similar to that used in well-known Bell state measurements, which we analyze using a conceptually transparent model of stochastic quantum trajectories; we use this to review photodetection, the most straightforward case, and then generalize to the diffusive trajectories from homodyne and heterodyne detection as well. Such quadrature measurement schemes are a realistic two-qubit extension of existing circuit QED experiments, which obtain quantum trajectories by homodyning or heterodyning a superconducting qubit’s spontaneous emission, or an adaptation of existing optical measurement schemes to obtain jump trajectories from emitters. We mention key results, presented from within a single theoretical framework, and draw connections to concepts in the wider literature on entanglement generation by measurement (such as path information erasure and entanglement swapping). The photon which-path information acquisition, and therefore the two-qubit entanglement yield, is tunable under the homodyne detection scheme we discuss, at best generating equivalent average entanglement dynamics as in the comparable photodetection case. In addition to deriving this known equivalence, we extend past analyses in our characterization of the measurement dynamics: we include derivations of bounds on the fastest possible evolution toward a Bell state under joint homodyne measurement dynamics and characterize the maximal entanglement yield possible using inefficient (lossy) measurements.

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通过连续荧光测量纠缠一对量子发射器：教程

我们讨论了在两个远程量子位之间产生量子纠缠的测量协议的最新发展，重点是联合连续检测其自发发射的理论。我们考虑一种类似于众所周知的贝尔态测量中使用的设备几何结构，我们使用随机量子轨迹的概念透明模型进行分析；我们使用它来回顾光电检测，这是最直接的情况，然后将其推广到零差和外差检测的漫射轨迹。这种正交测量方案是现有电路 QED 实验的实际双量子位扩展，通过零差或外差超导量子位的自发发射获得量子轨迹，或改编现有的光学测量方案以获得发射器的跳跃轨迹。我们提到了从单一理论框架内提出的关键结果，并在更广泛的关于通过测量生成纠缠的文献中的概念（例如路径信息擦除和纠缠交换）中建立了联系。在我们讨论的零差检测方案下，光子哪个路径信息获取是可调的，因此两个量子位纠缠产率是可调的，最多产生与可比光电检测情况相同的平均纠缠动力学。除了推导出这种已知的等价性之外，我们还扩展了过去的分析来描述测量动态特性：