Kiselev Alexei D, Ranim Ali, Rybin Andrei V
Laboratory of Quantum Processes and Measurements, ITMO University, Kadetskaya Line 3b, 199034 Saint Petersburg, Russia.
School of Physics and Engineering, ITMO University, Kronverksky Pr. 49, bldg. A, 197101 Saint Petersburg, Russia.
Entropy (Basel). 2022 Dec 5;24(12):1774. doi: 10.3390/e24121774.
We employ an exact solution of the thermal bath Lindblad master equation with the Liouvillian superoperator that takes into account both dynamic and environment-induced intermode couplings to study the speed of evolution and quantum speed limit (QSL) times of a open multi-mode bosonic system. The time-dependent QSL times are defined from quantum speed limits, giving upper bounds on the rate of change of two different measures of distinguishability: the fidelity of evolution and the Hilbert-Schmidt distance. For Gaussian states, we derive explicit expressions for the evolution speed and the QSL times. General analytical results are applied to the special case of a two-mode system where the intermode couplings can be characterized by two intermode coupling vectors: the frequency vector and the relaxation rate vector. For the system initially prepared in a two-mode squeezed state, dynamical regimes are generally determined by the intermode coupling vectors, the squeezing parameter and temperature. When the vectors are parallel, different regimes may be associated with the disentanglement time, which is found to be an increasing (a decreasing) function of the length of the relaxation vector when the squeezing parameter is below (above) its temperature-dependent critical value. Alternatively, we study dynamical regimes related to the long-time asymptotic behavior of the QSL times, which is characterized by linear time dependence with the proportionality coefficients defined as the long-time asymptotic ratios. These coefficients are evaluated as a function of the squeezing parameter at varying temperatures and relaxation vector lengths. We also discuss how the magnitude and orientation of the intermode coupling vectors influence the maximum speed of evolution and dynamics of the entropy and the mutual information.
我们采用热浴林德布拉德主方程的精确解，其刘维尔超算符同时考虑了动态和环境诱导的模间耦合，以研究开放多模玻色子系统的演化速度和量子速度极限（QSL）时间。随时间变化的QSL时间由量子速度极限定义，给出了两种不同可区分性度量变化率的上限：演化保真度和希尔伯特 - 施密特距离。对于高斯态，我们推导了演化速度和QSL时间的显式表达式。一般分析结果应用于双模系统的特殊情况，其中模间耦合可以由两个模间耦合矢量表征：频率矢量和弛豫率矢量。对于最初制备在双模压缩态的系统，动力学区域通常由模间耦合矢量、压缩参数和温度决定。当矢量平行时，不同区域可能与解纠缠时间相关，当压缩参数低于（高于）其温度相关临界值时，发现解纠缠时间是弛豫矢量长度的增（减）函数。或者，我们研究与QSL时间的长时间渐近行为相关的动力学区域，其特征是线性时间依赖，比例系数定义为长时间渐近比。这些系数作为压缩参数在不同温度和弛豫矢量长度下的函数进行评估。我们还讨论了模间耦合矢量的大小和方向如何影响演化的最大速度以及熵和互信息的动力学。
