Effect of entanglement embedded in environment on quantum non-Markovianity based on collision model

By means of collision models(CMs) where the environment is simulated by a collection of ancillas consisting of two entangled qubits, we investigate the effects of entanglement in the environment on the non-Markovianity of an open quantum system. Two CMs are considered in this study, in the first one the open quantum system S directly collides with the environment,while in the second one the system interacts with two intermediate qubits which, in turn, are coupled to the environment. We show that it is possible to enhance the non-Markovianity by environment entanglement in both models. In particular, in the second model, we show that the initial state of the auxiliary qubits can also affect the non-Markovianity of the system and there exists the optimal combination of the initial environmental state and the initial state of auxiliary qubits. In this case, the non-Markovianity can be greatly enhanced.     

Detecting Non-Markovianity via Linear Entropy of Choi State

Non-Markovian dynamics detection is one of the most popular subjects in quantum information science. In this paper, a linear -entropy-based non-Markovianity witness scheme is constructed. The positive definiteness of the Choi state will be broken in non-Markovian evolution, which can be witnessed by its linear entropy. Thus, the linear entropy of the Choi state can be used to witness non-Markovian dynamics. The effectiveness of the proposed method is verified using the pure dephasing channel as an example. Finally, it is shown that this method can be extended to the one based on Rényi entropy.     

利用量子相干性判定开放二能级系统中非马尔可夫性

从量子相干性包括l₁ norm相干性和量子相对熵相干性的角度建立了判定开放量子系统中非马尔可夫过程的方法, 并给出了相应的判别条件. 作为它们的具体应用, 研究了一个两能级系统分别经历相位衰减通道、 随机幺正通道和振幅耗散通道作用时对应的非马尔可夫过程发生必须满足的条件. 对于三种通道模型, 得到了l₁ norm相干性对系统任意态非马尔可夫过程发生的判别条件, 并发现在相位衰减通道和振幅耗散通道中其非马尔可夫过程发生 的条件与用其他方式如信息回流、可分性和量子互熵给出的条件是相同的, 而在随机幺正通道中给出了一个新的且不完全等价于基于信息回流和可分性对应的条件. 至于量子相对熵相干性, 在相位衰减通道中得到了对系统任意态的非马尔可夫过程发生的具体条件, 并发现该条件也等同于基于信息回流、可分性和量子互熵给出的条件. 而在随机幺正通道和振幅耗散通道中得到了系统最大相干态对应的非马尔可夫过程发生的条件.     

Effect of non-Markovianity on synchronization

We investigate the transient spontaneous quantum synchronization between two qubits interacting with a common non-Markovian environment based on a collision model. We are mainly interested in the effect of non-Markovianity on the synchronization between two qubits. We find that the non-Markovianity always delay the anti-synchronization and decrease the parameter region where the qubits get anti-synchronized. Meanwhile, we define V to characterize the visibility of synchronization and show that there is an apparent link among V, entanglement and quantum mutual information whether in the Markovian or non-Markovian regimes when the environment is in the vacuum state. Moreover, with the increase of temperature, the parameter region of the emergence of anti-synchronization and the time to get anti-synchronized in the non-Markovian regime gradually approaches that in the Markovian regime. The high temperature decreases the parameter region of the emergence of anti-synchronization in both Markovian and non-Markovian regimes, and breaks the connection among V, entanglement and quantum mutual information.     

Memory Effects in Quantum Dynamics Modelled by Quantum Renewal Processes

Simple, controllable models play an important role in learning how to manipulate and control quantum resources. We focus here on quantum non-Markovianity and model the evolution of open quantum systems by quantum renewal processes. This class of quantum dynamics provides us with a phenomenological approach to characterise dynamics with a variety of non-Markovian behaviours, here described in terms of the trace distance between two reduced states. By adopting a trajectory picture for the open quantum system evolution, we analyse how non-Markovianity is influenced by the constituents defining the quantum renewal process, namely the time-continuous part of the dynamics, the type of jumps and the waiting time distributions. We focus not only on the mere value of the non-Markovianity measure, but also on how different features of the trace distance evolution are altered, including times and number of revivals.     

Comparison between non-Markovian dynamics with and without rotating wave approximation

In the limit of weak coupling between a system and its reservoir,we derive the time-convolutionless(TCL) nonMarkovian master equation for a two-level system interacting with a zero-temperature structured environment with no rotating wave approximation(NRWA).By comparing the dynamics with RWA,we demonstrate the impact of RWA on the system dynamics,as well as the effects of non-Markovianity on the preservation of atomic coherence,squeezing,and entanglement.     

Non-Markovianity and Indivisible Quantum dynamics of a Apin-S System

Using a measure for the divisibility of a dynamical map,we study the non-Markovian character of a quantum evolution of a spin-S system,which is in an external field and weakly coupled to a bosonic bath with a certain temperature.The finite-temperature dynamics of the open system is obtained by the time-convolutionless master equation in the secular approximation.Besides the influence of the environmental spectral density function,the external field and low temperatures can afect the quantum non-Markovianity.It is found out that the non-Markovian feature of a dynamical map of a high-dimensional spin system is noticeable in contrast to that of a low-dimension spin system.     

Positivity and complete positivity of differentiable quantum processes

We study quantum processes, as one parameter families of differentiable completely positive and trace preserving (CPTP) maps. Using different representations of the generator, and the Sylvester criterion for positive semi-definite matrices, we obtain conditions for the divisibility of the process into completely positive (CP-divisibility) and positive (P-divisibility) infinitesimal maps. Both concepts are directly related to the definition of quantum non-Markovianity. For the single qubit case we show that CP- and P-divisibility only depend on the dissipation matrix in the master equation form of the generator. We then discuss three classes of processes where the criteria for the different types of divisibility result in simple geometric inequalities, among these the class of non-unital anisotropic Pauli channels.     

Non-Markovianity and Indivisible Quantum dynamics of a Apin-S System

Using a measure for the divisibility of a dynamical map, we study the non-Markovian character of a quantum evolution of a spin-S system, which is in an external field and weakly coupled to a bosonic bath with a certain temperature. The finite-temperature dynamics of the open system is obtained by the time-convolutionless master equation in the secular approximation. Besides the influence of the environmental spectral density function, the external field and low temperatures can affect the quantum non-Markovianity. It is found out that the non-Markovian feature of a dynamical map of a high-dimensional spin system is noticeable in contrast to that of a low-dimension spin system.