| Quantum information is one of the most active research in the field of physics,which exploits quantum resources such as entanglement to process and transmit information for high-speed computation and communication security.Recently,increasing the available Hilbert space in quantum information allows us to use less physical resources,improve channel capacity,noise-resistibility,computing speed,and error correction efficiency.Therefore,the study of quantum information in high-dimensional Hilbert space has attracted the attention of many scientists around the world.Photons are considered to be a very natural and excellent carrier of information in the field of quantum information.They have many advantages such as weak interaction with the environment,easy preparation and manipulation,and fast propagation speed.Furthermore,photons can also have complex spatial structures,and this additional degree of freedom leads to many fascinating properties,such as phase vortices and singularities,orbital angular momentum,and the possibility for high-dimensional Hilbert space.Therefore,exploiting the spatial structures of photons to study high-dimensional quantum information is the scope of this thesis.First,we present a flexible way to manipulate and separate the spatial modes of light,especially its radial modes.Our method is based on an interferometer with required accumulated Gouy phase difference,which can be intuitively understood in a geometric way.We successfully separate different radial modes into different outputs of the interferometer.For example,even and odd number of radial modes can bedistinguished.Our approach is very efficient and lossless.Combining several such interferometers would allow for access to a very large number of radial modes.The device can readily be used in multiplexing classical information,enrich the future research of high-dimensional quantum information using spatial modes of photons,and allow the applications of high-dimensional and multiphotonic quantum entanglement.Advances in controlling and shaping light have caused significant interests in the propagation of complex structured light,especially under realistic terrestrial conditions.While theoretical understanding of this research has significantly grown over the last two decades,outdoor-experiments with complex structured light are rare,and comparisons with theory have been nearly lacking.Such situations show a significant gap between theoretical models of atmospheric light behavior and current experimental effort.In an attempt to reduce this gap,we exploit a model that has been experimentally verified for the first time to investigate a general spatially structure light.We find that the effects of atmospheric turbulence are related to the chosen basis for encoding information.Our concrete numerical results will hopefully inspire experimental efforts and bring the theoretical and empirical study of complex light patterns in realistic scenarios closer together.It might be beneficial for future applications of free space optical communications classically as well as quantum.Second,quantum entangled states are an indispensable and important resource in all quantum information applications,especially high-dimensional entanglement means stronger non-locality.It is a natural way to realize these high-dimensional multiparticle entangled state using the spatial mode of light.However,how and which types of high-dimensional entanglement using spatial modes of photons can be experimentally produced are practical problems that need to be solved.Here,for the first time,we present a novel technique to deal with such questions,namely a hidden bridge between quantum optical experiments and graph theory.More specific,every quantum experiment using probabilistic photon pair sources can be rewritten as an undirected graph,and vice versa.The post-selected quantum state can be given by the coherent superposition of the perfect matching of the corresponding graph.With our powerful technique,we have successfully demonstrated how to experimentally prepare varioushigh-dimensional and multiphoton quantum entangled states,and use quantum experiments to explain theorems from graph theory.Furthermore,a crucial observation is that introducing complex weights in graphs naturally leads to quantum interference.Based on this,we identify an experimental unexplored multiphoton interference phenomenon.We then find that computing the results of such experiments is a classically intractable problem that cannot be effectively solved,which allows us to design a special purpose quantum computation – Boson Sampling.We can also describe linear optical quantum experiments that include a variety of linear optical components,and give new insights into quantum state generation with current photonic technology.In addition,we also show how to describe quantum protocols such as entanglement swapping in a graphical way.In the end,we introduce the concept of hypergraphs to describe quantum optical experiments with probabilistic multiphoton sources.Such general graph description provides new insights for producing complex multiphoton high-dimensional quantum entangled states,which go beyond limitations imposed by pair creation via spontaneous parametric down-conversion.The properties of hypergraphs can be investigated experimentally,for example,whether a hypergraph has a perfect matching can be answered by experimentally detecting multiphoton events in quantum experiments.By introducing complex weights in hypergraphs,we show a general many-particle quantum interference and manipulating entanglement in a pictorial way.Our approach is of great significance in the field of high-dimensional quantum information and paves the path for the development of multiphoton high-dimensional state generation.It might inspire new applications of quantum computations using hypergraph mappings and many exciting inventions and experimental demonstrations in the future. |
