Studies Of Quantum Information Processing In Spin Chain And Open System

Quantum information science is an emerging interdisciplinary research area that has applied the principles of quantum mechanics into information science research,and it has many advantages over traditional information science,which allows for the more secure transfer of data and greater efficiency in computations during quantum information pro-cessing.The absolute security of information transmission is physically guaranteed by the quantum state collapse and the no-cloning theorem in quantum information science.For example,in quantum key distribution,it is very effective for detecting the presence of eavesdroppers and fundamentally guaranteeing the security of information transfers.Ad-ditionally,when the basic principles of quantum mechanics are considered in the design of quantum algorithms,a vast improvement in the efficiency of computation can be ob-tained,such as the quantum Grover algorithm and the quantum Shor algorithm which have been successfully applied in increasing information search capacity and the decompo sition of int,egers into their primes,respectively.The quantum Shor algorithm represents such a breakthrough in the prime numbers decomposition of integers that many current encryption technologies are rendered no longer secure,and this undoubtedly is a challenge for cyber security in modern societies.In fact,quantum communication and quantum com-puting both rely on the quantum resources in their systems,and these quantum resources originate from various kinds of quantum correlations within the system,including quantum entanglement,quantum coherence,quantum discord,quantum fidelity,and so on.These quantum resources have been successfully applied into different quantum tasks.In real physical environments,a quantum system will unavoidably generate interactions with its surrounding environment,and because of the existence of the quantum decoherence effect,these interactions may reduce or even destroy the quantum correlations within a system.Thus,how to suppress the quantum decoherence effect and increase the quantum resources of the system has become an important research direction.The development of quantum information science has also made contributions to the research into quantum phase tran-sitions in condensed matter physics.Traditional research into quantum phase transitions requires an understanding of order parameters and symmetry breaking.However,it is dif-ficult to obtain the order parameters of a system.Fortunately,by making use of some concepts from quantum information theory,research into quantum phase transitions can be conducted relatively easily.In this thesis,we discuss how to use concepts from quantum information science to study the quantum phase transitions of many-body systems.We first utilize the density matrix renormalization group method to solve a one-dimensional extended quantum com-pass spin model and use multipartite entanglement to study the quantum phase transitions of the system.We find that multipartite entanglement is a good measure for detecting the quantum phase transitions,and the scaling behaviors of the multipartite entanglement are also obtained nearby the critical point.We then use trace distance and quantum coherence to study the quantum phase transitions of the one-dimensional extended quantum com-pass spin model,and also obtain accurate critical points of the quantum phase transitions and their corresponding scaling behaviors.Furthermore,the quantum phase transitions of the two-dimensional Kitaev honeycomb model is studied by making use of the quantum information theory methods.Through symmetry analysis of the two-dimensional Kitaev honeycomb model,we obtain the reduced density matrix of the model,and then utilize the quantum coherence based on the square root of the quantum Jensen-Shannon divergence to study the quantum phase transitions,and obtain the phase diagrams of the model in parameter space.The first derivative of the quantum coherence based on the square root of the quantum Jensen-Shannon divergence can effectively detect the quantum phase transi-tions,and their corresponding scaling behaviors can also be obtained through calculations.Additionally,we also use trace distance and relative entropy coherence to study the quan-tum phase transitions of the two-dimensional Kitaev honeycomb model,and find that they are also good measures for detecting the quantum phase transitions.The scaling behaviors of trace distance and relative entropy coherence of the two-dimensional Kitaev honeycomb model are also examined.We also discuss how to suppress the quantum decoherence effect and increase quan-tum correlations in the quantum system.Because of the existence of quantum decoherence,quantum correlations in quantum systems decrease and even disappear entirely,and this leads to the failure of various kinds of quantum tasks.We mainly discuss the effects of quantum-jump-based feedback and weak measurement along with quantum measurement reversal on the Rydberg atoms systems.We find that the effect of quantum-jump-based feedback can enhance the relative entropy coherence of the system,which provides evidence that decoherence effect in Rydberg atoms systems can be suppressed by quantum-jump-based feedback.We also discuss the influence of the quantum-jump-based feedback on the occupation number of the system,and find that quantum-jump-based feedback can reduce the spontaneous radiation effect of the system.This may be the reason why this method can suppress the decoherence effect of the Rydberg atoms system.We then proceed to discuss the effect of quantum-jump-based feedback on the quantum coherence based on the square root of the quantum Jensen-Shannon divergence and the uncertainty relation of the system,and find that quantum-jump-based feedback can enhance the quantum coherence based on the square root of the quantum Jensen-Shannon divergence,and reduce the un-certainty bound of the system.We also find that weak measurement along with quantum measurement reversal can enhance the quantum coherence of the Rydberg atoms system,reduce the uncertainty and uncertainty bound of the system and enhance the quantum entanglement of the system.