The Study Of Quantum Coherence And Entanglement By Using Respective Concurrence Measures

Quantum information science has seen an explosive development in recent years,particularly within the past two decades.In the field of quantum information,quantum entanglement is viewed as an important physical resource.It plays a key role in quantum information processing and has wide applications such as quantum cryptography,quantum teleportation,and dense coding.A basic and longer standing problem in the theory of quantum entanglement is to distinguish quantum entangled states from the separable one.It has attracted great interest in the last twenty years,and rich research achievements have been gained.Another burgeoning field of quantum information science is the study of quantum coherence.As a fundamental feature of the quantum mechanics,quantum coherence arising from the principle of quantum superposition plays an important role in quantum physics.It is an essential ingredient for numerous physical phenomena such as quantum optics,quantum thermodynamics,quantum biology etc.Quantum coherence is also regarded as an key resource for quantum information processing tasks.Recently,a rigorous framework to quantify coherence from the view of theory of physical resource was presented,and have attracted enormous attentions of researchers.In this setting,quantum coherence is considered to be a resource that can be characterized,quantified,and manipulated in a manner similar to quantum entanglement.Considerable effort has been devoted to investigate the field of quantum coherence,and a number of research findings have been proposed.Quantum entanglement and quantum coherence both are stem from the superposition principle,and are of fundamental significance for the quantum theory.They are also important quantum resources for quantum computation and quantum information.It is then natural to investigate the potential link between these two quantum resources.The main content of this thesis is derived form the thinking on above issue.We put forward a new physically meaningful and mathematically rigorous measure of coherence,coherence concurrence,and then establish a rigorous and general framework for the interconversion between two quantum resources,coherence and entanglement,by constructing the relationship between coherence concurrence and famous entanglement concurrence.Our work provides a clear quantitative and operational connection between coherence and entanglement.Besides,before we present the above central result,we report our findings on theory of entanglement.In the aspect of entanglement detection,we present some necessary and sufficient product criteria for quantum states based on the rank of realignment matrix of density matrix,and they are necessary and sufficient separability criteria for pure states.In the case of entanglement quantification,we provide several lower bounds of concurrence for multiqubit systems,and prove that if the multipartite concurrence is larger than a certain value,then the state must be 6)-nonseparable.The above results both can be applied to detect 6)-nonseparable in some context.In the last,we focus on the issue of quantifying the quantumness of quantum ensembles.We propose a class of measures to quantify the quantumness in a general quantum ensemble,and discuss the applications of these measures in different branches of quantum information,especially in quantum coherence,entanglement and correlation.Our findings provide a new viewpoint to understand these quantum resources from the perspective of quantumness of ensemble.This thesis is organised as follows:In chapter 1,we review the main concepts of quantum theory,include quantum states,quantum measurements and operators,reduced density operator and so on.In chapter 2,we introduce our findings on theory of entanglement after a short review of entanglement.We give some necessary and sufficient product criteria for quantum states based on the rank of realignment matrix of density matrix.As a special case,these criteria can determine 6)-separability or 6)-nonseparability of a multipartite pure state.Then,we provide the lower bounds of multipartite concurrence and can be applied to detect the multipartite 6)-nonseparable states.At the same time,we present an exact formula of concurrence for some mixed quantum states.In chapter 3,we report our results about coherence measure and the relationship between coherence and entanglement.First,we introduce basic knowledge of quantum coherence.Then,we define a new coherence measure based on generalized Gell-Mann matrices,and rigorous proof shows that the new coherence measure,coherence concurrence,fulfills all the requirements of coherence measures.In the last,we establish a link for the interconversion between coherence and entanglement by constructing the relationship between coherence concurrence and famous entanglement concurrence.In chapter 4,we investigate the issue of quantumness of quantum ensemble.We define a class of measures of quantumness of ensemble by using unitary similarity invariant norms of commutators of the constituent density operators of an ensemble,and discuss their applications in the theory of quantum information.