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dynamics of Entanglement in open quantum system with markovian and non-markovian behavior

Robabeh Abdi Someh

Published Jan 1, 2017• 0 citations
OpenAlex

Abstract

In general, quantum systems can be divided into two groups of closed quantum systems and open quantum systems. Also open quantum systems are divided into two categories of Markov systems (non-memory) and non-Markov systems (memory). To distinguish these two behaviors, we use of the entanglement dynamic which can provide a lot of information about the evolution of a system. Returning information from environment to system can be translate as increasing of entanglement in specific period of times, so if increase of entanglement seen, system will have non-Markov treatment and if there is uniform reduction in entanglement, there will be Markov treatment. In special problems which have special matrixes, we have to calculate entanglement every time. For this purpose, we will use of incidence that is a scale for entanglement. For qubit systems the formation of incidence is close which called entanglement of formation. Numerical computation is done by MATLAB and FORTRAN and entanglement dynamics varying by time will be gained. Then analyzing of diagrams is done and the type of process such as Markov and non-Markov is recognized. MENFIT that can show treatment of entanglement in every time, is used too.

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In general, quantum systems can be divided into two groups of closed quantum systems and open quantum systems. Also open quantum systems are divided into two categories of Markov systems (non-memory) and non-Markov systems (memory). To distinguish these two behaviors, we use of the entanglement dynamic which can provide a lot of information about the evolution of a system. Returning information from environment to system can be translate as increasing of entanglement in specific period of times, so if increase of entanglement seen, system will have non-Markov treatment and if there is uniform reduction in entanglement, there will be Markov treatment. In special problems which have special matrixes, we have to calculate entanglement every time. For this purpose, we will use of incidence that is a scale for entanglement. For qubit systems the formation of incidence is close which called entanglement of formation. Numerical computation is done by MATLAB and FORTRAN and entanglement dynamics varying by time will be gained. Then analyzing of diagrams is done and the type of process such as Markov and non-Markov is recognized. MENFIT that can show treatment of entanglement in every time, is used too.
The question, whether an open system dynamics is Markovian or non-Markovian can be answered by studying the direction of the information flow in the dynamics. In Markovian dynamics, information must always flow from the system to the environment. If the environment is interacting with only one of the subsystems of a bipartite system, the dynamics of the entanglement in the bipartite system can be used to identify the direction of information flow. Here we study the dynamics of a two-level system interacting with an environment, which is also a heat bath, and consists of a large number of two-level quantum systems. Our model can be seen as a close approximation to the 'spin bath' model at low temperatures. We analyze the Markovian nature of the dynamics, as we change the coupling between the system and the environment. We find the Kraus operators of the dynamics for certain classes of couplings. We show that any form of time-independent or time-polynomial coupling gives rise to non-Markovianity. Also, we witness non-Markovianity for certain parameter values of time-exponential coupling. Moreover, we study the transition from non-Markovian to Markovian dynamics as we change the value of coupling strength.
The question, whether an open system dynamics is Markovian or non-Markovian can be answered by studying the direction of the information flow in the dynamics. In Markovian dynamics, information must always flow from the system to the environment. If the environment is interacting with only one of the subsystems of a bipartite system, the dynamics of the entanglement in the bipartite system can be used to identify the direction of information flow. Here we study the dynamics of a two-level system interacting with an environment, which is also a heat bath, and consists of a large number of two-level quantum systems. Our model can be seen as a close approximation to the `spin bath' model at low temperatures. We analyze the Markovian nature of the dynamics, as we change the coupling between the system and the environment. We find the Kraus operators of the dynamics for certain classes of couplings. We show that any form of time-independent or time-polynomial coupling gives rise to non-Markovianity. Also, we witness non-Markovianity for certain parameter values of time-exponential coupling. Moreover, we study the transition from non-Markovian to Markovian dynamics as we change the value of coupling strength.
The thesis is contributed to the study of the decoherence dynamics of dissipative qubit systems. We reveal the profound impact of the formation of a bound state between the qubit and its local environment on the decoherence dynamics of qubit system in non-Markovian regime. We find that the decoherence can be suppressed greatly under the non-Markovian dynamics when the bound state is formed. Consequently, the entanglement can be partially preserved in the steady state. A criterion on this decoherence/disentanglement suppression is given explicitly. It can give a useful guideline on the decoherence control in experiment. We also find that the entanglement can be stably distributed among all components and particularly it always satisfies an identity. Our unified treatment includes the previous results in the literatures as special cases. The result reveals the profound nature of the entanglement and should have significant implications for quantum information processing.
Open quantum systems are often encountered in many different physical situations. From quantum optics to statistical mechanics, they are fundamental in the understanding of a great variety of different phenomena. Some of the most common examples are the relaxation to equilibrium, the existence of nonequilibrium stationary states, and the dynamics of atoms in interaction with electromagnetic fields. A crucial step in the analysis is to consider the quantum open system and its environment as the two mutually interacting components of a larger isolated system. Thereafter, the so‐called Markov approximation is often considered, which consists on assuming that the time scales associated to the dynamics of the quantum open system are larger than those of the environment. It is the interplay of the different time scales associated with the system and the environment what determines the validity of the different approximations made. In this paper we will discuss the dynamics of a open quantum system in contact with a reservoir when the Markov approximation is not valid, and we have to include some non‐Markovian or memory effects.
The temporal evolution of entanglement between a noisy system and an ancillary system is analyzed in the context of continuous-time open quantum system dynamics. Focusing on a couple of analytically solvable models for qubit systems, we study how Markovian and non-Markovian characteristics influence the problem, discussing in particular their associated entanglement-breaking regimes. These performances are compared with those one could achieve when the environment of the system is forced to return to its input configuration via periodic instantaneous resetting procedures.
Knowledge of the dynamical behavior of correlations with no classical counterpart, like entanglement, nonlocal correlations and quantum discord, in open quantum systems is of primary interest because of the possibility to exploit these correlations for quantum information tasks. Here we review some of the most recent results on the dynamics of correlations in bipartite systems embedded in non-Markovian environments that, with their memory effects, influence in a relevant way the system dynamics and appear to be more fundamental than the Markovian ones for practical purposes. Firstly, we review the phenomenon of entanglement revivals in a two-qubit system for both independent environments and a common environment. We then consider the dynamics of quantum discord in non-Markovian dephasing channel and briefly discuss the occurrence of revivals of quantum correlations in classical environments.