AI 中文总结
研究如何计算罗比内特状态，提出用完全正定、高精度且不依赖外部求解器的数值离散化方案，通过扩展随机主方程为系统+传输线设置来实现，经测试验证了该方法在具有挑战性例子上高达10阶的精度，并提供了物理见解。
AI 中文摘要
从零差或外差测量中获得的真正连续量子轨迹只能近似重构。在任何模数转换步骤中，精确重构所需的连续测量信号会在有限时间间隔Δt的区间上进行平均。最近引入了仅根据此离散记录进行的最佳重构，即罗比内特状态。本文展示了如何用一种完全正定、在Δt中精度可达任意高阶且不依赖任何其他外部求解器的数值离散化方案来计算罗比内特状态。我们的推导依赖于将随机主方程扩展为一个系统+传输线设置，通过测量传输线的“零模”来得到罗比内特状态。我们在一个具有随机哈密顿量和跳跃算子的具有挑战性的例子上测试了该方法，并验证了其高达10阶的精度。除了数值意义外，我们的方法还提供了丰富的物理见解，特别是扩展了Wonglakhon、Chantasri和Wiseman最近关于纯度的结果，这些结果很难通过其他方式获得。
英文摘要
Truly continuous quantum trajectories, obtained from homodyne or heterodyne readouts, can only ever be reconstructed approximately. The continuous measurement signal, needed for exact reconstruction, is averaged over bins of finite time $Δt$ during any analog to digital conversion step. The best reconstruction possible, knowing only this discrete record, was introduced recently and dubbed the Robinet state. In this article, we show how the Robinet state can be computed with a numerical discretization scheme that is completely positive, accurate to arbitrarily high order in $Δt$, and that does not rely on any other external solver. Our derivation relies on a dilation of the stochastic master equation into a system + transmission line setup, constructed in such a way that measuring what we call the "zero mode" of the line yields the Robinet state. We test the method on a challenging example with random Hamiltonian and jump operator, and verify its accuracy up to order $10$. Apart from its numerical interest, our approach provides a wealth of physical insights, extending in particular recent results on purity obtained by Wonglakhon, Chantasri, and Wiseman, that would be difficult to obtain in any other way.
Comments53 pages, 4 figures. Added Author Contributions section
