Quantum Correlations For Bipartite Continuous-variable Systems

Operator algebra and operator theory are important branches of functional analysis,and have a profound background in quantum mechanics,especially in the quantum infor-mation science arisen in recent years.In particular,many questions of quantum mechanics and quantum physics need to be solved by means of operator theory and operator algebra.In quantum communication,quantum entanglement is an important physical resource and plays a major role in quantum information processing tasks.With the development of quantum information and quantum computing,quantum correlations beyond entan-glement had become important quantum resource in quantum information processing.This thesis mainly uses operator algebra and operator theory to discuss several quantum correlations for continuous-variable systems,characterizes their properties and effects in quantum information processing.1.Firstly,two quantum correlations Q and QP for(m + n)-mode continuous-variable systems are introduced in terms of average distance between the reduced states under the local Gaussian positive operator-valued measurements(GPOVMs),and analytical formulas of these quantum correlations for Gaussian states are obtained.We show that the product states do not contain these quantum correlations;and conversely,every(m + n)-mode Gaussian states with zero quantum correlations are product states.In addition,several equivalences of two-mode Gaussian states being product states are given.Generally,it is difficult to compute Q and QP.It is easily seen that Q>QP.However,Q(?AB)=QP(?AB)holds for any two-mode Gaussian state ?AB,and a computable formula for Q(?AB)is given.Q(QP)is also compared with Gaussian geometric discord for symmetric squeezed thermal states,and for most cases,Q(QP)is better than Gaussian geometric discord to detect the quantum correlation.Lastly,we study the evolution in noisy channel of Q(QP)for two-mode Gaussian states.2.Luo[Phys.Rev.Lett.,2011,106,120401]introduced the measurement-induced nonlo-cality(MIN)for finite-dimensional systems,which is a new quantum correlation.Hou,Guo[J.Phys.A:Math.Theor.,2013,46,325301]extended this notation to infinite-dimensional systems.Here,we discuss MIN in terms of von Neumann measurement for Gaussian states and show that a Gaussian state has no this kind of MIN if and only if it is a product state.It is difficult to calculate MIN for general Gaussian states.However,we get the analytic formulas of MIN for any two-mode squeezed vacuum states,two-mode squeezed thermal states and mixed thermal states.In spirit of Gaussian quantum discord,we discuss how to introduce Gaussian MIN by GPOVMs.In fact,by means of the properties of Weyl op-erators and characteristic functions,we prove that,different from the Gaussian quantum discord,there exists no local GPOVMs preserving reduced state invariant,and so there is no Gaussian version of MIN by GPOVMs.3.The quantum nonclassicality induced by local unitary operators is one of the most important topics.The discriminating strength Ds(?AB)induced by local Gaussian unitary operators for any(1 + 1)-mode Gaussian state ?AB is introduced by Rigovaccain L.[Phys.Rev.A,2011,83,042325].Here,we further discuss the quantity based on Gaussian unitary operators by restricting to Hilbert-Schmidt norm and get analytic formulas of Ds for two-mode squeezed thermal states and mixed thermal states.The change of the quantity DS(?AB)-Ds((I(?)?)(?AB))after some special Gaussian channels ? are also discussed.Lastly,we give another measure based on a new fidelity,and discuss the quan-tity DSF(?AB)induced by Gaussian unitary operators with respect to this measure,and compare it with Gaussian geometric discord.It is found that our quantity DSF(?AB)can contain more quantum correlations.