Research On Measurement And Generation Of Hyper-entangled State

As an almost indispensable key resource,quantum entanglement has been widely used in quantum communication in the past decades,such as quantum teleportation,quantum secure direct communication.Different to the entanglement in single degrees of freedom(DOF),Hyperentanglement means simultaneous entanglement in more than one DOF.Hyperentanglement can be used to realize the complete Bell state analysis,high capacity dense coding,quantum secure direct communication and deterministic quantum repeaters.In the application of entanglement,the users should first know the information of the entanglement.Several methods have developed to quantify or measure the entanglement,such as entanglement witnesses,quantum state tomographic reconstruction.On the other hand,hyperentanglement sources have been considered as an important resource in the field of quantum information processing.Therefore,the generation of hyperentanglement source has become an important research hotspot in the field of quantum information processing.This paper provide two protocols for measuring the concurrence of hyperentangled state and generating of hyperentanglement source.The work is as follows:In this paper,we first provide a protocol for measuring the concurrence of two photon six qubit hyperentangled state.In the protocol,the concurrence measurement in the three DOFs are independent.The total concurrence of the hyperentangled state equals to the sum of the concurrence in each DOF.We require two same initial hyperentangled state.With the help of the QND gate constructed by the cross-Kerr nonlinearity and some linear optical elements,the concurrence in each DOF can be converted to the success probability of distilling specified quantum state.Even if the measurement in one DOF fails,it will not affect the concurrence measurement of other DOFs.In addition,with the development of quantum communication,the research on hyperentangled states is not only focused on concurrence of hyperentangled state,but also on the generation of hyperentangled states.In the second part of this paper,we propose a scheme for the generation of hyperentangled state with three DOFs by studying the generation of hyperentangled state.The scheme is based on the SPDC process to generate entangled photon pairs,so as to use quantum interference on the beam splitter to achieve hyperentangment in space,polarization,and discrete frequency DOF.The protocol may play an important role in future quantum information processing.