The Study Of Manipulation On Quantum Entangled States In Optical Systems

As a unique phenomenon and an irreplaceable source in the quantum world,quantum entanglement plays a significant role in quantum information processing.At present,among the feasible physical systems proposed,optical system is generally favored among the feasible physical systems proposed.The photon is considered as the chief candidate for quantum information carrier.On the one hand,it can realize transmission in free space,has fast transmission speed,weak coupling with the environment,and is easy to be controlled by optical components.Moreover,the application technology of optical fiber is mature,simple and with high fidelity.On the other hand,the photon has more than one degree of freedom,such as polarization,spatial-mode,orbital angular momentum,time-energy,frequency,etc.These different degrees of freedom can carry information at the same time.Hyper-entanglement,the entanglement in multiple degrees of freedom of a photon system simultaneously,can improve the capacity and security of quantum communication.However,the photon has the disadvantage that it is difficult to realize the direct interaction between photons.With only linear optical elements,it is not only inefficient and complicated,but also mostly nondeterministic to complete optical quantum information processing.Cross-Kerr nonlinearity can make photons interact with each other,this will provide an ideal platform for deterministic optical quantum information processing.This dissertation is to study how to realize the manipulation of entangled quantum states in optical systems with linear optical elements and cross-Kerr nonlinearity,including the fusion of W states,the concentration,purification and analysis of hyper-entangled states.The content of the whole dissertation is divided into the following four parts:In chapter 1,we introduce some preliminary knowledge related to the research content,including quantum states,quantum measurements,linear optical elements,weak cross-Kerr nonlinearity and so on.In chapter 2,we first present an optical scheme to fuse two small-size polarization entangled W states into a large-scale W state without qubit loss.That is,with the assistance of linear optical elements,cross-Kerr nonlinearity and X homodyne measurement,the present scheme can fuse an 9)-qubit W state and a 8)-qubit W state to get an(9)+ 8))-qubit W state.Based on similar physical ideas,we then propose a qubit-loss-free fusion scheme for fusing three polarization entangled W states simultaneously.The elements of a two-outcome positive-operator valued measurement and the appropriate joint unitary operation for realizing POVM measurement are given.As an example,the corresponding physical realization setup in the optical system is proposed.At the end of the two schemes,we analyze the success probability and the resource cost of each scheme,as compared to the previous work.It is concluded that the resource cost of our two fusion schemes is less,the steps of fusion can be greatly reduced,and it is feasible in experiment.In chapter 3,we studies the hyper-entanglement concentration and purification.The establishment of quantum entangled channel is the precondition of quantum long-distance communication.With hyper-entanglement,the capacity of quantum communication can be improved.However,in the real process of transmission,a noisy environment often disturbs an entangled state and thus makes it collapse into a non-maximally entangled one or even a mixed state.This will degrade the fidelity and security of quantum communication.Entanglement concentration and purification are two effective methods to deal with the influence of environmental noise.We present both hyper-entanglement concentration and purification protocols for nonlocal two-photon systems in polarization,time-bin,and spatial-mode degrees of freedom.In two hyper-entangled concentration schemes: the first protocol extracts a maximally hyper-entangled Bell state with nonlinear optics,which is discussed in two cases of unknown and known coefficients;the second protocol is used to concentrate an initial partially hyper-entangled state based on the parameter splitting method with only linear optical elements,where coefficients of the initial state are known.The hyper-entanglement purification protocol is constructed with two steps resorting to Polarization-Time-Spatial parity-check operation using the quantum nondemolition detector and SWAP gates,respectively.With this purification protocol,the bit-flip errors in the three degrees of freedom can be corrected with high efficiency.In chapter 4,the measurement and analysis of entangled states is the key procedure to read the encoded information.Hyper-entangled state analysis is an important part of high capacity quantum communication.Based on the analysis of the existing states analyzers,we present two deterministic hyper-entangled state analysis protocols for photons entangled in polarization,spatial-mode and time-bin degrees of freedom.The first protocol is a hyper-entangled Bell state analyzer.The core is to construct polarization parity check P-QND and spatial-mode parity check S-QND with linear optical elements,cross-Kerr nonlinearity and X homodyne measurement,which can completely distinguish polarization and spatial-mode Bell states.With the help of the polarization entanglement information,the time-bin Bell state can be completely distinguished.We generalize the idea to analyze the three-photon hyperentangled GHZ states.In each scheme,a set of mutually orthogonal hyper-entangled basis states are completely discriminated via three steps.