Study On Enhancement And Protection Of Non-Classical Effects In Non-Hermitian Quantum Systems

Non-classical effects are some peculiar quantum effects different from classical physics,which results from the interaction between quantum systems,such as quantum entanglement,quantum discord,quantum coherence,quantum speed limit,atomic squeezing effect,quantum Fisher information,and so on.Non-classical effects of quantum systems as available physical resources have broad prospects for applications in research fields of quantum optics and quantum information,and have been widely concerned by researchers.However,there are two significant problems in the generation of non-classical effects at present: The first one is that the intensity of non-classical effects which is only produced by the interaction between quantum systems alone is weak;The other one is that the inevitable interaction between quantum systems and surrounding environments leads to the decoherence of quantum systems,and makes non-classical effects of quantum systems easy to be destroyed.Therefore,how to enhance non-classical effects of quantum systems,how to restrain the decoherence to protect non-classical effects of quantum systems from the impact of quantum noises have always been difficult issues in the research fields of quantum optics and quantum information.On the other hand,in conventional studies of quantum mechanics,a Hamiltonian of a quantum system must be represented by a Hermitian operator,which is in order to ensure that the eigenvalues of the Hamiltonian of the system are real,and the time evolution of the system is unitary.In recent years,with non-Hermitian quantum theories have been gradually systematized,researches on quantum properties of non-Hermitian quantum systems have also attracted extensive attention.Can we use the special properties of non-Hermitian quantum systems to enhance and protect non-classical effects of quantum systems? This thesis makes use of the special properties of non-Hermitian quantum systems to investigate the enhancement and protection of non-classical effects of quantum systems,and some innovative results are obtained.The main research contents and results are as follows:In Chapter 1,firstly,the research background is introduced.Then,several typical non-classical effects of quantum systems and the basic theory of non-Hermitian quantum systems are expounded.In Chapter 2,the geometric measure of quantum discord and the negativity as a measure of quantum entanglement as two kinds of typical measures of quantum correlations for a two-qubit entangled system under a local non-Hermitian operation are investigated.Our results show that,the local non-Hermitian operation not only can partially protect quantum correlations of the system,but also can enhance quantum correlations of the system to the maximum value under appropriate conditions.This kind of evolutionary behavior that quantum correlations of the system can be increased under the local non-Hermitian operation appears to violate conventional properties of quantum correlations which formulate that quantum correlations of the system are invariants under local operations,which is mostly aroused by the non-Hermiticity of the local operation.In Chapter 3,the quantum coherence of a two-qubit entangled system under a local non-Hermitian operation is investigated.Basing on the basis-independent relative entropy coherence measure,a theoretical scheme to realize the complete recovery of quantum coherence of the system from the decoherence caused by the amplitude damping noise channel via the local non-Hermitian operation is proposed.Our results show that quantum coherence of the system can be effectively governed by the non-Hermitian operation,even can be completely recovered from the decoherence under the proper choice of the non-Hermiticity parameter.In Chapter 4,the quantum speed limit time of a non-Hermitian two-level system is investigated.Numerical calculations demonstrate that,with respect to the quantum evolution between two distinguishable quantum states of the nonHermitian quantum system,the evolutionary time does not have a non-zero lower bound.Our results show that,the quantum evolution of the system can be effectively accelerated by adjusting the non-Hermiticity parameter,as well as the quantum speed limit time can be arbitrarily small even be zero.In Chapter 5,the entropy squeezing of a two-level atom in the well-known Jaynes-Cummings model under a non-Hermitian operation is investigated,and a theoretical scheme to generate the sustained optimal entropy squeezing of the atom via the non-Hermitian operation is provided.Our results show that,the atomic entropy squeezing effect can be remarkably enhanced by performing the non-Hermitian operation,the squeezing degree and the persistence time of the entropy squeezing of atomic polarization components are closely related to the non-Hermiticity intensity of the non-Hermitian operation.Especially,even if the initial state of the atom is without any entropy squeezing,the sustained optimal entropy squeezing of the atom also can be generated via an appropriate nonHermitian operation.In Chapter 6,the quantum Fisher information of a two-level system under a non-Hermitian operation and the depolarization is investigated.Our results show that the evolutionary behavior of quantum Fisher information of the system can be effectively controlled by the non-Hermitian operation.Especially,through choosing the optimal input state and a low depolarizing probability,the quantum Fisher information of the system can be significantly increased by an appropriate nonHermitian operation,and the precision of parameter estimation can be remarkably enhanced.In Chapter 7,conclusions and outlooks are presented.