Studies On Quantum Information Processes Based On Polar Molecules And Entropic Uncertainty Relation

It is an important challenge for quantum information processing to find a re?liable physical system which can be encoded,manipulated easily and has a long coherent time.Polar molecules take advantage of neutral atoms and trapped ions,which can maintain coherence for a long time and have the long-range tun-able dipole-dipole interaction.Moreover,the rich internal energy level structure of polar molecules can encode more quantum information,and the larger per-manent electric dipole moment makes it easier to be controlled by the external fields.Therefore,polar molecules can be used as a very promising physical car-rier in quantum information processing.In recent decades,people have made remarkable achievements in the fields of cold molecule preparation,trapping and manipulation,which lay the significant foundation for the realization of quantum information processing based on polar moleculesAs a vital quantum resource,quantum entanglement and quantum coher-ence have a wide range of applications in quantum communication and quantum computing.In this thesis,the pendular states of polar molecules in electric fields are used as qubits.The aim is to study non-classical effects such as quantum entanglement,quantum discord,and quantum coherence in polar molecular sys-tems,and explore the feasibility of scalable quantum computing based on polar molecules.Considering that general physical systems cannot completely isolate from the external environment,the influences of environmental noises on the dy-namic behaviors of molecular systems are analyzed.Furthermore,by combining with optimal control theory and numerical calculations,we try to realize some multi-bit quantum logic gates and quantum algorithms using the pendular states In addition,we also preliminarily discuss the quantum-memory-assisted entropic uncertainty relation and quantum entanglement in the framework of relativity The research content of this thesis mainly includes the following four sections1.Study on the quantum correlation and quantum coherence of dipole-coupled ultra-cold polar molecules and their intrinsic decoher-ence process.By solving the Hamiltonian of the polar symmetric top molecule in the electric field,we first select the appropriate pendular states as the qubit-s.Then considering the dipole-dipole interaction,we explore the relationships of the quantum correlations and quantum coherence between the coupled top molecules with the electric field,ambient temperature and dipole-dipole interac?tion.The results show that both quantum entanglement and quantum discord are inversely proportional to the electric field strength and directly proportional to the dipole coupling strength,and will be destroyed by higher ambient temper-atures.However,the functional relation between the coherence of the system and the electric field is not monotonous,but first increases and then decreases with the field intensity.In addition,by solving the Milburn equation,it is found that the system of the top molecules being initially in the(|01>+|10>)/(?)is more robust than the one being initially in the(|00>+|11>)/(?),which can be better against the intrinsic noise.Moreover,although the time-dependent evolutions of the entanglement and the coherence of top molecular system are quite similar,the systemic coherence may still exist when the entanglement is completely de-stroyed by noise.Furthermore,we examine the EPR steering of the linear polar molecular system,and find that the steerability between the linear molecules is consistent with the quantum correlations of top molecular system in some degree2.Using optimal control theory to realize the control of entan-glement and coherence as well as the three-bit quantum computation in polar molecular systems.By taking the pendular states of dipole-coupled BaI molecules in electric field as an example,the appropriate laser pulses are designed to drive the transitions from systemic ground state to the maximal-ly entangled Bell states(|00)+|11>)/(?)and(|01>+|10>)/(?)with the help of optimal control.Then,the target state is set to the maximal coherent state 1/2(|00)+|01>-|10>+|11>).The corresponding control pulse is obtained through optimization,and the degree of systemic coherence can be enhanced.Moreover,the conversion between entangled state and coherent state can also be realized by designing optimal field.Subsequently,the optimal control theory is extended to the situation of multiple target states,and the phase constraints are considered Employing three SrO molecules arranged in a chain as a carrier,we design control fields to implement three-bit Toffoli gate,quantum adder and quantum Fourier transform in one step.Finally,we optimize the laser pulse sequence composed of Hadamard gate,Oracle gate and Diffusion gate,and successfully simulate the three-bit Grover search algorithm.3.Evolution of the coherence and the entropic uncertainty relation of the dipole system driven by the light field in a noisy environment at infinite temperature.Combining the theory of coherent resources and the quantum-memory-assisted entropic uncertainty relation,we can obtain the unilateral coherent inequality for multiple measurements.The dipole system is assumed to be in the infinite temperature environment,and to interact with the external radiation field.By solving the master equation,we obtain the time-dependent evolution of the upper and lower bounds of the systemic coherent inequality.The results show that the unilateral coherence of the dipole system in the limit of infinite temperature will gradually decrease with time.The detuning of the light field will lead to multiple oscillations of the evolutionary behavior,and the oscillation process can be adjusted by the Rabi frequency.In addition,we also give the evolution of the entropic uncertainty and the concurrence of the dipole system.By comparison,we can find that the lower the coherence of the system is,the higher the uncertainty of the entropy is.The internal reason is that the quantum entanglement between the dipoles is destroyed during the evolution.4.Dynamics and steering of the quantum-memory-assisted entrop-ic uncertainty relation and the entanglement in the back ground of relativity.The intersection of quantum information theory and general relativ-ity,quantum field theory,and string theory can not only improve the quantum theory itself,but also promote the understanding of space-time concepts and localized causality.We assume that the measured particle is located in asymp-totically flat spacetime,and the quantum memory is located near the Garfin-kle-Horowitz-Strominger dilation black hole.And the effect of black hole di-lation on the quantum-memory-assisted entropic uncertainty relation is explored.The results show that as the dilation parameter increases,the accessible entropic uncertainty outside the black hole horizon grows monotonously,and the inacces-sible entropic uncertainty inside the black hole horizon drops monotonously.In the increasing process of dilation parameter,the entanglement between the mea-sured particle and each mode inside(outside)the horizon is redistributed,but the total amount of quantum entanglement in the system remains unchanged.In addition,with the help of weak measurement reversal operation,it is possible to achieve the steering of the entropic uncertainty relation for partially entangled state.By choosing the appropriate reversal measurement intensity,the entropic uncertainty that is physically available can be effectively reduced.