Two Kinds Of Continuous-variable Entanglements And Their Implementing In Solid-state Quantum Circuit

Continuous-variable(CV)quantum information processing(QIP)has become the powerful alternative of discrete-variable QIP because its advantage of efficient implementation in preparing,manipulating,measuring,etc.As the key resource of CV QIP,CV entanglement has then attracted much attention.It has been applied to various quantum information and quantum communication protocols,the schemes to produce it have been explored in different systems such as the electromagnetic field,solid resonators,atomic ensembles,nuclear spins,Josephson junctions,and Bose-Einstein condensates.Among them,the best-known example is optical system,in which various schemes of CV QIP have been adequately explored and the CV entanglement even up to10,000-qumode has recently been prepared.In comparison,fewer schemes for implementing CV entanglement have been proposed in solid-state system,although the solid-state based encoding of CV systemsoffers promising perspectives for performing quantum computation.Solid-state system,especially the circuit quantum electrodynamics(QED)system can promise good scalability and allows robust control,storage,and readout due to their strong interaction with external fields.Circuit QED also allows for rapid,repeated nondemolition qubit measurement and can be an excellent test-bed for implementing quantum feedback control.These advantages indicate that the circuit QED could provide promising perspectives for QIP with practical way.Therefore the studies on the circuit QED have received extensive attention over the past few years,in which preparing and manipulating entangled states are important tasks.However,up to now,the majority of the studies have been focused on the discrete schemes,with the CV ones having less progress.1.We study a system of three superconducting transmission line resonators coupled with four-level qubit in a circuit quantum electrodynamics system.By analyzing the correlation between the energy transition of the four-level qubit system and the driving of classical fields and the coupling of resonators,we show that an effective tripartite continuous-variable entanglement could be realized in the three solid resonators by using the adiabatic eliminated method.2..We present a general description of continuous-variable perfect maximally entangled statese(PMES)? The way to obtain this kind of states is shown by applying beam splitter operations on continuous-variable EPR states.We show that the approximate version of these states can be achieved in circuit quantum electrodynamics systems composed of electrical superconducting resonators and rfSQUIDs by tuning the applied flux bias to the rfSQUIDs.