開放量子系統過程的非馬可夫程度、系統資訊回流以及系統環境關聯

馬可夫過程是指外來的狀態僅跟現在有關,對於度量開放量子系統中的馬可夫程度,一般是基於量子資訊從環境回流至系統來度量,然而,這種方法與古典系統中的定義並不一致,最近與古典馬可夫定義一致的度量被提出,我們關注這新的定義, 並且指出在這新的定義下,一個馬可夫系統等價於沒有以下兩種效應, 一是資訊從環境約化密度矩陣回流至系統,二是沒有系統環境化約矩陣的關聯. 其中第二種效應可以不帶任何的系統資訊, 我們給出這兩種效應的若且唯諾條件並且給出度量以及演算法. 除此之外我們還定義了系統環境關聯, 並給出僅有系統環境關聯的演算法. 並且將理論應用在四種物理模型上. 我們發現在短時間內非馬可夫性近似環境約化密度矩陣的資訊回流效應, 在長時間範圍, 似環境約化密度矩陣的資訊回流效應或僅有系統環境關聯效應的其中之一會佔據主導地位, 最後,我們給出沒有資訊回流的操作型定義.

關鍵字

馬可夫過程；系統環境關聯；密度矩陣

並列摘要

A Markovian process of a system is defined classically as a process in which the future state of the system is fully determined by only its present state, not by its previous history. There have been several measures of non-Markovianity to quantify the degrees of non-Markovian effect in a process of an open quantum system based on information backflow from the environment to the system. However, the condition for the witness of the system information backflow does not coincide with the classical definition of a Markovian process. Recently, a new measure with a condition that coincides with the classical definition in the relevant limit has been proposed. Here, we focus on the new definition (measure) for quantum non-Markovian processes, and characterize the Markovian condition as a quantum process that has no information backflow through the reduced environment state (IBTRES) and no system-environment correlation effect (SECE). The action of IBTRES produces non-Markovian effects by flowing the information of quantum operations performed by an experimenter at earlier times back to the system through the environment, while the SECE can produce non-Markovian effect without carrying any earlier quantum operation information. We give the necessary and sufficient conditions for no IBTRES and no SECE, respectively, and show that a process is Markovian if and only if it has no IBTRES and no SECE. The quantitative measures and algorithms for calculating non-Markovianity, IBTRES, and solely SECE are explicitly presented. We also apply the theorem to the spin-boson model. We develop four spin-boson system with different bath spectral densities or system-environment coupling Hamiltonians. The non-Markovianity has a similar pattern to the IBTRES in the short time period. In long time limit, either the solely correlation effect or the IBTRES becomes more important, and a simple relationship between non-Markovianity, IBTRES and solely SECE can be found. Finally, we classify the information pathways into three different pathways and give an operational meaning of system information backflow from the environment.