Preparation Of Multi-photon Entangled States Via Quantum Random Walk

Quantum entanglement plays an important role in quantum computation and quantum communication.Because the structure of multipartite entangled states is more complex than that of bipartite counterparts,their preparation is more difficult.W state and GHZ state that exhibit genuine multipartite entanglement are two inequivalent three-qubit entangled states,and they cannot be converted into each other by local operations and classical communication(LOCC).How to effectively achieve the construction of multipartite entangled quantum states using the existing physical systems is an important question.Although solid state system are the preferred systems for quantum computing,photonic system as flying bits are the preferred systems for quantum communication.Thus,we will focus on optical systems in this thesis.The existing coupling mechanisms for photons are based on beam splitter(BS),but once BS is successfully fabricated,its parameters cannot be modified,which greatly limits the application scope of BS-based coupling mechanism for photons.Therefore,it is fundamentally interesting to design new coupling mechanisms for photons without BS.Quantum walk is a generalization of classical random walk in quantum field.In an optical quantum walk,the photons with orthogonal polarization states will walk to different positions,respectively.The control characteristic of quantum random walk from photon polarization degree of freedom to space position degree of freedom makes it possible to couple photons.In this thesis,we design a photon coupling mechanism without BS by virtue of the control characteristic of quantum walk,and design physical schemes to generate multi-photon entangled states based on this mechanism.The main results of this thesis are as follows:1.Two schemes based on quantum random walk is proposed to generate three-photon W state and four-photon Cluster state.In these schemes,each photon has its own spatial degree of freedom.After the quantum walk,photons of different polarizations will enter paths of different locations,and the appropriate path-swap and post-selection operations would make the photons evolved into target entangled states.The coupling mechanism between photons of our schemes is realized by simple photonic path-swap operations instead of BS,which makes the scheme easier and more feasible.2.Three simplified schemes based on quantum random walk are proposed to generate three-photon W state and GHZ state and four-photon Cluster state.Compared with the preparation schemes with each photon occupying an independent degree of freedom of spatial mode,these schemes are based on three photons sharing the same spatial mode,which greatly reduces the use of optical elements and the operation error of the whole scheme.In addition,no auxiliary photons are required and path-swap and post-selection operations will realize the coupling of photons in the polarization degree of freedom.3.As a generalization of the preparation scheme of three-photon W state,the preparation protocol of N-photon W state is proposed.In principle,this scheme can be extended to the preparation of multi-photon W states of arbitrary number.The calculations show that the scheme is still theoretically feasible when the number of photons reaches 50.