标题： 在因果条件量子测量规定下的半经典引力现象学 II：海森堡绘景和表观光学纠缠 显示英文标题

标题： Semiclassical gravity phenomenology under the causal-conditional quantum measurement prescription II: Heisenberg picture and apparent optical entanglement

摘要： 由半经典引力影响的量子态演化与量子引力理论中的演化不同，这是由于存在一个依赖于状态的引力势。 这种依赖于状态的势引入了态演化的非线性，其理论被称为薛定谔-牛顿（SN）理论。 在半经典引力理论背景下，理解量子态上连续量子测量过程的形式化方法已在论文I [1]中使用薛定谔绘景进行了讨论。 在本工作中，开发了一种使用海森堡绘景的等效形式化方法，并将其应用于分析两种旨在测试引力量子性质的光机械实验协议。 SN理论的海森堡绘景形式化方法有助于研究这些协议中输出光场的协方差矩阵以及进一步的纠缠特性。 我们发现，在SN理论中，连续量子测量下两个镜子的量子轨迹之间的经典引力可以引起输出光场的明显纠缠（尽管镜子之间没有量子纠缠），这可能作为设计用于探测由量子引力引起的纠缠的实验的假警报。 显示英文摘要

摘要： The evolution of quantum states influenced by semiclassical gravity is distinct from that in quantum gravity theory due to the presence of a state-dependent gravitational potential. This state-dependent potential introduces nonlinearity into the state evolution, of which the theory is named Schroedinger-Newton (SN) theory. The formalism for understanding the continuous quantum measurement process on the quantum state in the context of semiclassical gravity theory has been previously discussed using the Schr\"odinger picture in Paper I [1]. In this work, an equivalent formalism using the Heisenberg picture is developed and applied to the analysis of two optomechanical experiment protocols that targeted testing the quantum nature of gravity. This Heisenberg picture formalism of the SN theory has the advantage of helping the investigation of the covariance matrices of the outgoing light fields in these protocols and further the entanglement features. We found that the classical gravity between the quantum trajectories of two mirrors under continuous quantum measurement in the SN theory can induce an apparent entanglement of the outgoing light field (though there is no quantum entanglement of the mirrors), which could serve as a false alarm for those experiments designed for probing the quantum gravity induced entanglement.