开放量子系统的状态主方程可以分解为由随机主方程描述的随机轨迹。这样的随机微分方程可以被解释为一个更新公式的系统状态条件下获得的结果，从监测浴。到目前为止，对于由具有$L$ Lindblad项的主方程描述的系统的任意扩散解（由高斯白噪声监测产生的量子轨迹），只找到了一种参数化（数学表示）[H. M. Wiseman和A. C. Doherty，Phys. Rev. Lett. { \bf 94}，070405（2005）]。这种参数化，我们称之为U-代表，参数化扩散unravellings的$L^2+2L$实数，安排在一个矩阵${\sf U}$受到三个约束。在本文中，我们研究扩散测量的替代参数化。我们发现，而令人惊讶的是，描述扩散unravellings可以统一的一个单一的方程为非正方形复杂的矩阵，如果一个人愿意允许一些冗余的提升所需的实参数从$L^2+2L$到$3L^2+L$。我们称这种参数化为M-rep。M-rep和U-rep都缺乏测量应该是什么样子的物理图像。因此，我们提出了另一个参数化，B-REP，详细说明了如何测量分束器，移相器，和零差检测器。不同的表示之间的关系推导。
英文摘要：
The master equation for the state of an open quantum system can be unravelled into stochastic trajectories described by a stochastic master equation. Such stochastic differential equations can be interpreted as an update formula for the system state conditioned on results obtained from monitoring the bath. So far only one parameterization (mathematical representation) for arbitrary diffusive unravellings (quantum trajectories arising from monitorings with Gaussian white noise) of a system described by a master equation with $L$ Lindblad terms has been found [H. M. Wiseman and A. C. Doherty, Phys. Rev. Lett. {\bf 94}, 070405 (2005)]. This parameterization, which we call the U-rep, parameterizes diffusive unravellings by $L^2+2L$ real numbers, arranged in a matrix ${\sf U}$ subject to three constraints. In this paper we investigate alternative parameterizations of diffusive measurements. We find, rather surprisingly, the description of diffusive unravellings can be unified by a single equation for a non-square complex matrix if one is willing to allow for some redundancy by lifting the number of real parameters necessary from $L^2+2L$ to $3L^2+L$. We call this parameterization the M-rep. Both the M-rep and U-rep lack a physical picture of what the measurement should look like. We thus propose another parameterization, the B-rep, that details how the measurement is implemented in terms of beam-splitters, phase shifters, and homodyne detectors. Relations between the different representations are derived.
Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院量子材料与技术研究所）；Institut für Theorie der Kondensierten Materie, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院凝聚态理论研究所）
We review the continuous monitoring of a qubit through its spontaneous emission, at an introductory level. Contemporary experiments have been able to collect the fluorescence of an artificial atom in a cavity and transmission line, and then make measurements of that emission to obtain diffusive quantum trajectories in the qubit's state. We give a straightforward theoretical overview of such scenarios, using a framework based on Kraus operators derived from a Bayesian update concept; we apply this flexible framework across common types of measurements including photodetection, homodyne, and het…
We investigate entanglement dynamics in continuously monitored open quantum systems featuring current-carrying non-equilibrium states. We focus on a prototypical one-dimensional model of boundary-driven non-interacting fermions with monitoring of the local density, whose average Lindblad dynamics features a well-studied ballistic to diffusive crossover in transport. Here we analyze the dynamics of the fermionic negativity, mutual information, and purity along different quantum trajectories. We show that monitoring this boundary-driven system enhances its entanglement negativity at long times, …
Princeton University（普林斯顿大学）；Laboratoire de Physique de l’École Normale Supérieure, CNRS, ENS & Université PSL（巴黎高等师范学院物理实验室，法国国家科学研究中心，巴黎文理研究大学）；University of Geneva（日内瓦大学）
Entanglement generation and preservation is a key task in quantum information processing, and a variety of protocols exist to entangle remote qubits via measurement of their spontaneous emission. We here propose feedback methods, based on monitoring the fluorescence of two qubits and using only local pi-pulses for control, to increase the yield and/or lifetime of entangled two-qubit states. Specifically, we describe a protocol based on photodetection of spontaneous emission (i.e. using quantum jump trajectories) which allows for entanglement preservation via measurement undoing, creating a lim…
