| Quantum coherence is an important physical resource.Because it is an impor-tant premise for realizing quantum communication and quantum information,it is widely used in modern information processing tasks as people accumulate experience in microcosm.In 1998,Professors Bender and Boettcher of the University of Washington gave the concepts and properties of PT-symmetry and complete PT-symmetry,and proved that the eigenvalues of Hamiltonian with complete PT-symmetry are real numbers,this new discovery has a real physical meaning and background,and has received extensive attention from scholars at home and abroad.The characterization of pure and mixed states in PT-symmetry quantum theory and the evolution of states in PT-symmetry theory has achieved results.However,the concept,nature and portrayal of coherence in non-self-adjoint quantum mechanics have not been given,which is also the main problem solved in this paper.This article is divided into three chapters,the specific content is as follows:The first chapter first gives some of the symbols used in this paper,and some basic concepts,assumptions and theorems of PT-symmetry and quantum coher-ence,and introduces their development process,research significance and current situation.The sccond chapter first introduces the coherence of the Tpure state based on the l1 norm metric in the PT-symmetric quantum system.Secondly,the expres-sion of the coherence of the pure state in the PT-symmetric quantum system is given.Then introduces the coherence of pure states in two different PT-symmetric quantum systems.Finally,the correlation is given by examples.The conclusion is explained.The third chapter introduces the coherence of the pure state and the coherence of the pure state based on the geometric coherence metric in the PT-symmetric quantum system.The relative entropy metric and geometric coherence in the PT-symmetric quantum system are obtained.The corresponding characterization of the coherence of the pure state under the metric. |
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