Theoretical Study Of Quantum Infor-Mation Processing In The Open And Spin-chain Systems

Quantum information science,as an interdisciplinary,covers physics,math and informatics.It is mainly based on the principles of quantum mechanics which is different from the classical in-formatics following the principles of classical physics.Quantum mechanics is the crystallization of wisdom of Human exploring the world over the last century,which not only helps us under-stand our world,but also provides the foundation for the development of science and technology in the future.In this era of information explosion,the artificial intelligence,the big data,and the Internet have all stepped into the periods of vigorous developments.The desires for computer performance and security of information transmission are also growing stronger.However,the development of computer chips has approached the bottleneck which means the classic computer performance will reach its limit in the coming decades.Therefore,how to explore new types of computers and new methods of information transmission has become more urgent.As an alterna-tive,the quantum information science has attracted a lot attention and developed quickly in both theoretical and experimental researches in recent years.It inherit people's vision for the next gen-eration of computers and communications.The quantum correlation is important resources in the processes of realizing many quantum information tasks.Nevertheless,the quantum resources are very fragile and easily destroyed by the decoherence effect induced from the surrounding envi-ronment.The decoherence is one of the major obstacles to the practical application of quantum information processing.In this sense,it is necessary to study the dynamics of quantum correlation in open quantum systems and the ways to prevent or minimize the influences of environmental noises.On the other hand,quantum phase transitions(QPTs)are an important phenomenon in the condensed matter physics and have draw lots of attention.How to reveal and characterize the crit-ical phenomenons of quantum many-body systems is an important task and becomes a hot topic in condensed-matter physics.Traditional methods mainly focus on the identification of the order parameters and the pattern of symmetry breaking.The recent developments in quantum informa-tion theory have given some insights into the QPTs.Specifically,the quantum fidelity,quantum correlation and trace distance have been successfully used as effective tools to reveal the QPTs without any prior knowledge of order parameters.In this thesis,we apply the Monte Carlo wave function method to study the effect of quantum-jump-based feedback on the dynamics of quantum discord for two non-interacting two-level atoms coupled to a single-mode of the cavity field with and without the rotating wave approximation.It is found that the counter-rotating terms can be helpful for generating steady states and the value of steady-state quantum discord can be increased to approach the maximum in the long-time limit by feedback controls.We also explore the influence of the time evolutions of mean excitation number in total system and atomic subsystem on the quantum correlations and show that the enhancement of mean excitation number in atomic subsystem by feedback controls leads to the high value ofsteady-state quantum discord.On the other hand,we investigate how to control the quantum evo-lution speed in a quantum system consisting of a qubit locally coupled to its finite-temperature environment with Ohmic-like spectrum.It is found that the high temperature not only leads to the speed-up but also speed-down processes in the weak-coupling regime,which is different from the strong-coupling case where only exhibits speed-up process,and the effects of Ohmicity pa-rameter of the bath on the quantum evolution speed are also different in the strong-coupling and weak-coupling regimes.Furthermore,we realize the controllable and stationary quantum evolu-tion speed by applying the bang-bang pulse,and examine the influence of the bath temperature and Ohmicity parameter on the quantum evolution speed in the whole decoherence process.We also study the quantum evolution speed of a qubit in a nonlinear bath by resorting to the hierar-chical equations of motion method beyond the Born-Markov approximation.It is shown that the performances of quantum evolution speed in weak-coupling and strong-coupling regimes are also different.In particular,the quantum evolution speed can be decelerated by the rise of temperature in the strong-coupling regime which is an anomalous phenomenon and contrary to the common recognition that quantum evolution speed always increases with the temperature.Another research topic in this thesis is the use of the metrics in quantum information science to study the QPTs of many-body systems.We investigate the multipartite entanglement and trace distance of the one-dimensional anisotropic spin-1/2 XXZ spin chain with the Dzyaloshinskii-Moriya interaction and find that the Dzyaloshinskii-Moriya interaction can influence the entan-glement distribution and increase the proportion of multipartite entanglement in the entanglement structure.Furthermore,we explore the quantum phase transition of the XXZ spin chain with Dzyaloshinskii-Moriya interaction by making use of the multipartite entanglement and trace dis-tance along with the quantum renormalization-group method.It is found that the first derivatives of renormalized multipartite entanglement and trace distance for the ground state have dramatic changes near the critical point,and the renormalized multipartite entanglement and trace distance obey the universal finite-size scaling laws in the vicinity of the quantum critical point.Finally,we turn to the quantum phase transitions of high-dimensional many-body systems.We employ multipartite entanglement and quantum coherence to investigate the quantum phase transitions of the transverse-field quantum Ising model on the triangular lattice and Sierpinski fractal lattices.It is shown that the behaviors of the multipartite entanglement and quantum coherence closely relate to the quantum criticality of these high-dimensional models.As the thermodynamic limit is approached,the first derivatives of multipartite entanglement and quantum coherence exhibit sin-gular behaviors and the consistent finite-size scaling behaviors for each lattice are also obtained from the first derivatives.The multipartite entanglement and quantum coherence are demonstrated to be good indicators for detecting the quantum phase transitions in the triangular lattice and Sier-pinski fractal lattices.Furthermore,we explore the relations between critical exponents and the correlation length exponents for these models,and find that the critical exponents are not only directly related to the correlation length exponents in the vicinities of the critical points,but also depend on the space or fractal dimensionalities of lattices.