Research On The Dynamics Of Quantum Entanglement In Several Typical Environments

Quantum entanglement is the most core resource for quantum information.The tasks that classical information source cannot complete can be realized by the resource,such as quantum teleportation,quantum dense coding and quantum cryptography and so on.During the operation of the quantum system in the entangled state,to keep the initial entanglement to the maximum value is one of the preconditions to realize the quantum information process and quantum computation by using quantum entanglement.However,the real quantum systems can not be completely isolated from the environment.The unavoidable coupling of the quantum system with the surrounding environment will lead to quantum decoherence,which is a major obstacle to the realization of quantum information processing.So,to find a way to keep maximal entanglement in operation is the motivation of this paper.Recently,a new method,weak measurement,has been proposed to protect quantum entanglement in a large number of literatures.It can obtain some weak signals that cannot be measured before by the combination of the pre-and post measurements,so as to explain the strange phenomenon caused by these small changes.Therefore,the study of entanglement dynamics in various environmental models,particularly the open quantum systems with non–zero temperature heat baths,not only have great theoretical interests in understanding the concept of quantum entanglement but also have potential application values in quantum information processing and quantum computing.The environment studied in this paper includes different quantum channels and thermal baths,and the main contents include the following aspects:1.We investigate the entanglement protection of a qutrit–qutrit system under local amplitude damping channels by weak measurement and reversal measurement.We examine?-type of initially entangled states.We find that the negativity and the purity have opposite behavior and the qutrit–qutrit entanglement decays as the decoherence strength increases.Special attention is paid to how to protect the quantum entanglement from decoherence by weak measurement and reversal measurement.Our results show that we can defeat amplitude damping decoherence by the combination of prior weak measurement and post optimal weak measurement reversal comparing with the dynamics without protection.Regardless of the value of decoherence,the protection scheme has better effect on V–configuration like.And with the increase of decoherence strength,the difference is more obvious.In addition,we also find that the enhancement of entanglement is very weak when decoherence strength is zero.2.We investigate the effect of the weak measurement and reversal measurement on the protection of the entanglement for an entangled two–qutrit system from four typical quantum noisy channels,i.e.,amplitude damping channel,phase damping channel,bit flip channel and depolarizing channel.Given the parameters of the qutrits'state,it is found that the weak measurement and reversal measurement indeed helps for protecting entanglement in some quantum channel.In addition,we discuss how the negativity and the success probability behave with the weak or measurement reversal strength changing.3.We investigate the dynamics and protection of quantum entanglement of a qutrit–qutrit system under local amplitude damping channels with finite temperature.We consider two different initial states.We find that the qutrit–qutrit entanglement decays monotonically as the decoherence strength increases,and may go through entanglement sudden death at higher temperature.Special attention is paid to how to protect the quantum entanglement from decoherence by weak measurement and reversal measurement.Our results show that the entanglement increases with the increase of weak measurement strength when the temperature is lower.However,the protections of entanglement by weak measurement and reversal measurement are almost failed and the decays of entanglement goes up with the increase of weak measurement strength for different decoherence strength when the temperature is higher,even entanglement suffers sudden death.4.We investigate the entanglement for an entangled two–qubit pure state from four typical quantum noisy channels with memory,i.e.,amplitude damping channel,phase damping channel,bit flip channel and depolarizing channel,based on the quantum technique of the weak measurement and reversal.For the initial state |??=a|00?+d|11?,it is found that the weak measurement and reversal operation indeed helps for protecting entanglement from the above four quantum channels with memory.But for the Bell–like initial state |??=b|01?+c|10?,the weak measurement and reversal operation only protects entanglement in the amplitude damping channel with memory.Whether |?? or |??,we also find that the initial entanglement could be drastically amplified and the memory effects play a significant role in the suppression of entanglement sudden death and protection of entanglement under severe decoherence in contrast to the results of memoryless quantum noisy channels.In addition,we discuss the relationship between the concurrence,the memory parameter,the weak measurement strength and the reversal weak measurement strength.5.We study the steady–state entanglement and heat current of two coupled qubits,in which one qubit is connected with either two baths with the different temperature?the temperature of the bath-a is T₁,and the temperature of the bath-b is T₂?or a bath.We construct the master equation in the eigenstate representation of two coupled qubits to describe the dynamics of the total system and derive the solutions in the steady–state with strong coupling regime between them.We have discussed the variations of the steady–state entanglement with respect to various parameters of the system in both equilibrium and non–equilibrium cases.We find that the coupling strengths and the energy detuning as well as the temperature gradient are beneficial to the enhancement of the entanglement in equilibrium case.In the non–equilibrium case,when T₁>T₂,the temperature gradient is useless for the entanglement;forT₁<T₂,when the temperature gradient is smaller?larger?,which has a positive?negative?effect on the entanglement.We also study the heat current of the two coupled qubits and their variations with the energy detuning,coupling strengths and diverse temperature of the heat baths.The energy detuning has a positive?negative?effect on the heat current in the low?high?temperature;heat current decreases?increases?with coupling strengths increases for a given temperature when T₁>T₂?T₁<T₂?.The temperature of cool bath is lower,the heat current is larger.6.We study the steady–state entanglement and heat current of two coupled qubits without rotating wave approximation in the calculation,in which two qubits are connected with two independent heat baths?IHBs?or two common heat baths?CHBs?.We construct the master equation in the eigenstate representation of two coupled qubits to describe the dynamics of the total system and derive the solutions in the steady–state with stronger coupling regime between two qubits than qubit–baths.We will not make rotating wave approximation in the calculation for the qubit–qubit interaction so that we are able to investigate the behavior of the system in both the strong and weak coupling regimes.In the strong coupling regime,we find that the entanglement decreases with the increasing bath temperature?energy detuning?in equilibrium baths.In the non–equilibrium baths,the temperature gradient is useful?useless?for the enhancement of the entanglement with?without?rotating wave approximation under low average temperature.We also study the heat current of the two coupled qubits and their variations with the energy detuning,coupling strengths and diverse temperature of the heat baths.The temperature is lower,heat current is larger.Heat current increases?decreases?with coupling strengths when the temperature of one bath is lower?higher?than the other.And the energy detuning leads to a positive?negative?effect when the temperature is low?high?.In the weak coupling regime,the entanglement increases with coupling strengths and decreases with the heat bath temperature?energy detuning?increasing.When the temperature of one bath is lower?higher?than that of the other one,in the case of IHBs,the heat current firstly decreases?increases?and then increases?decreases?with the increase of coupling strength,while the heat current increases?decreases?with coupling strengths increasing under the CHB case.