The Analysis Of Quantum Evolution Speed Limit Based On Quantum Spin System

As the rapid development of quantum information theory in recent years,especially the research in the fields of quantum computation,quantum communication,and quantum control,there is further knowledge for people about the time limitation on quantum system evolution.Due to the fact that the quantum uncertainty relation is one of the fundamental principles in quantum mechanics,the energy and time uncertainty relation for quantum system which stems from the previous principle limits the evolution time of all the quantum systems,i.e.,the maximum speed for the evolution of a system.The lower limit of time is called quantum speed limit(QSL)time for a system.Originally,the research objects are aim at closed quantum systems,and people got a general expression of the QSL time.Hereafter,more studies about this problem are extended to open quantum system which is more useful in reality and discuss the factors in influencing the evolution speed.Quantum spin system,a typical quantum model,has been extensively utilized in many quantum information regions,and the research about its QSL time is meaningful and practical.Therefore,in this article,we will study the QSL time of some representative quantum spin systems and discuss the possible accelerating mechanism for every model.There are three parts in the whole thesis.In the first part,we research a typical non-Markovian model,i.e.,quantum central spin model.We discover that when the central qubit couples with its surrounding bath environment,it is susceptible to the external magnetic field and the coupling strength,and suitable values of parameters can induce the reduce of QSL time.Moreover,we investigate the effect from the number of spins in bath and find the QSL time would decrease until saturate as the bath going to the thermodynamic limit.For searching forthe intrinsic accelerating reason,we research the excited population of central spin with the change of coupling strength and find the correlation between population and QSL time,hence we interpret the critical function on acceleration of evolution.In the second part,we consider the QSL time as a characterization of the feature of a system.In the research of a central spin interacting with a Lipkin-Meshkov-Glick(LMG)bath,we find that under the condition of suitable external spin numbers and coupling strength,the point that the central system endures from no speedup to speedup is just the point that quantum phase transition happens which is from the symmetry broken phase to symmetric phase.In addition,by numerically calculating the non-Markovianity of system,we get it has opposite correlation with the QSL time as the parameter varying,which verifies that the non-Markovian nature has positive influence on the evolution speed of a system.Meanwhile,the transition from Markovian to non-Markovian also occurs at the quantum phase transition point.In the third part,we have an investigation about the QSL time of the spins in a finite XY spin chain.For a system of which initial state is at equilibrium,when the external transvers magnetic field abruptly turns off from a certain value,which we called magnetic field quench,the system will begin evolving.We discover that for the QSL time of single-site qubit,the transvers magnetization is a potential factor for its evolution.As for the nearest-neighbor spins,it is found that the entanglement between the two particles is an important resource for speeding up the system evolution.Besides,we also get the QSL time of the next-nearest-neighbor qubits and find since the entanglement between them is limit,the other parameters,such as the quenched magnetic field and anisotropy parameter show the effectiveness on accelerating the quantum evolution.