Basis-independent Quantum Coherence Measure And Investigation Of Quantum Coherence Of PT-symmetric Systems

In recent years,quantum coherence of quantum system and quan-tal features of non-Hermitian system have attracted more attention.Quantum coherence originating from quantum superposition exhibits quantum-interference effect of quantum state,and it is the most fun-damental and the most important quantum resource in quantum infor-mation theory.Moreover,quantum coherence plays a key role in many emerging science fields such as quantum information theory,quantum metrology,Nano thermodynamics,and quantum biology.The most im-portant things in quantum coherence researches are quantifying quan-tum coherence.In present,researches of quantifying quantum coherence are made important progress,and many ways of quantifying quantum coherence are proposed.However,all most of quantum coherence mea-sures are basis-dependent does not accord with physical reality,since the physical properties of the physical system should not be changed with the different choice of coordinate systems.On the other hand,non-Hermitian PT-symmetric quantum system is powerful tool for study-ing quantum open systems and expends fields of quantum mechan-ics.Researches of non-Hermitian system have attracted more attention,however,researches of quantum coherence of PT-symmetric quantum system are a few.Therefore,this article proposes basis-independent quantum coherence measure and studies quantum coherence of PT-symmetric quantum system by using quantum coherence theory and theory of non-Hermitian quantum system.The main research contents and innovations are as follows:In the first chapter,the main content of chapter is fundamental theory of coherence.The coherence of electromagnetic field is induced,which is defined by coherence function in history.Moreover,the re-source theory of quantum coherence,which is discussed and analyzed in detail in this chapter,is frontier domains in quantum information investigations.In the second chapter,the basic theory of open quantum system is briefly introduced.Firstly,the definitions of closed quantum system and open quantum system are discussed.Then,an effective description of open quantum system is induced by non-Hermitian quantum mechanics,and master-equation method of open quantum system is investigated in detail.Finally,the property of PT-symmetric system is introduced.In the third chapter,firstly,we have discussed some defects in previ-ous basis-dependent quantum coherence measures.Then,by redefining the maximum classical mixture state as a complete incoherent state,i.e.,it is the accurate and unique zero-coherence state for the finite dimensional Hilbert space.Next,we have presented an intrinsic basis-independent quantum coherence measure(IBIQCM),which can reflect the intrinsic quantum coherence property of the quantum state itself,by using the relative entropy.The IBIQCM satisfies all the conditions of the resource-theoretic framework of quantifying coherence.Moreover,the new IBIQCM reveals physical essence of quantum coherence that is degree of order of the quantum state,and simplifies the calculation of quantum coherence measure.In the fourth chapter,we investigated the quantum coherence of two-level PT-symmetric system in open quantum system.Our results show that,quantum coherence can be created by PT-symmetric sys-tems,even if the initial state of the two-level system is the complete incoherent state.Even though two-level system is interacted with dis-sipative environments,the quantum coherence exhibits a long-lived re-vival,and can be protected.We find that the two-level system can obtain more coherence with the coupling strength ? increases.And we should point out that the PT-symmetric system can be regarded as a good candidate system for creation of the long-lived quantum coherence in dissipative environments.In the fifth chapter,summary and outlook of the full text are pre-sented.