Preparation And Application Of Non-Gaussian States Based On Parametric Down Conversion And Conditional Measurement

The preparation of quantum states is one of the major problems in quantum computation and quantum information processing.For discrete quantum states,due to the difficulty in preparing and manipulating them in experiments,physicists are forced to turn their attention to continuous-variable quantum states.Although the continuous-variable Gaussian quantum state is relatively easy to manipulate experimentally,it is not enough to meet the requirements for the preparation of highly nonclassical,highly entangled and strongly decoherent quantum states.In recent years,with the flourish of quantum information science,it has been found that the non-Gaussian states play an important role and have a good application prospect in quantum coding,quantum teleportation,quantum images and quantum precision measurement,which can be prepared by means of parametric down-conversion,conditional measurement and non-Gaussian operation.Driven by this advantage,we in this thesis propose some preparation schemes of a new non-Gaussian state based on parametric down-conversion and condition measurement,and then make full use of the non-classical and entanglement measurement methods to comprehensively analyze the nature of the non-Gaussian states.Under the Braunstein and Kimble scheme,the applications of these quantum states in quantum teleportation are investigated.The specific research work of this thesis can be summarized as follows:Firstly,based on the input of coherent states,a novel non-Gaussian state —Laguerre polynomial excited coherent state(LPECS)— is proposed by using the parametric down-conversion and the condition measurement.According to Glauber-Sudarshan P function,photon number distribution,Q function,second-order correlation function,squeezing effect and Wigner function,the non-classicality of LPECS is discussed in detail.It is found that the LPECS presents obvious non-classical properties which can be modulated by a coherent state amplitude,a squeezing parameter,and a conditional measurement.In particular,there is a more pronounced non-classicality in terms of the squeezing effect and the Wigner function.Secondly,a new type of two-mode non-Gaussian state—the Laguerre polynomial weighted squeezed vacuum state(LPWSVS)is introduced by applying the parametric down-conversion and the condition measurement into each mode of the two-mode squeezed vacuum state.The entanglement property of the LPWSVS is discussed by using entanglement entropy,EPR correlation,squeezed effect and the fidelity of teleportation.Our results show that only the entanglement entropy can be improved by both single-and two-mode conditional measurement in a small squeezing region,while the other properties can be improved only by the two-mode conditional measurement including symmetrical and asymmetrical cases.A comparison among these properties shows that the squeezing and the EPR correlation definitely lead to the improvement of both the entanglement entropy and the fidelity,and the region of enhanced fidelity can be seen as a sub-region of the enhanced entanglement which means that the entanglement is not always beneficial for the fidelity.In addition,the effect of photon-loss after condition measurement on the fidelity is considered,and the symmetrical two-photon conditional measurement may present better behavior than the symmetrical single-photon case against the decoherence in a certain region.Finally,by using two kinds of two-mode squeezed vacuum as input states,a novel non-Gaussian state—two-mode squeezed Laguerre polynomial excited vacuum state(TMSLPEVS)— is prepared based on the beam splitter and the condition measurement.In particular,for single photon conditional measurements,the generation of the TMSLPEVS can be reduced to the theoretical squeezed Bell state,and the entanglement property of the TMSLPEVS is investigated through the entanglement entropy and the EPR correlation.Our results show that by modulating several different parameters,such as photon number,transmissivity,squeezing parameter,the entanglement entropy and the EPR correlation can always be improved.