| Non-classical effects of quantum states of light are strongly relative to the study of quantum communication and quantum computation at present. In the quantum key distributions of quantum cryptographic systems, such as the protocols of BB84 and B92, the high quality single photon source, which emits antibunching photon one by one, is necessary. In addition, Ekert's twin photon protocol is based on the generation of entangled photon pairs. The squeezed effects of light take also very important roles in continuous variable quantum cryptography, and so on. In fact, generation and distribution of quantum keys are the processes of preparing and manipulating quantum states. On the other hand, studying the evolution properties of quantum states is helpful for manipulating them. It is well known that the Wigner function of quantum states contain their many messages, such as the probability distributions and phases. Thus, reconstructing the Wigner function of the studied quantum states is very important.Non-classical effects of quantum states have been extensively studied in experiments due to their many potential applications. The relevant theoretical study are important for the possibly experiment. In this thesis, we focus our theoretical study on the non-classical effects of some quantum states, such as the photon-added and photon-depleted even/odd coherent states and the photon-added squeezed vacuum states. The results show that both photon-added and photon-depleted even/odd coherent states and photon-added squeezed vacuum states appear antibunching effects. However, the photon-depleted even/odd coherent states show the squeezed effects, but photon-added even/odd coherent states did not.Secondly, we reconstruct the Wigner function of the photon-added and photon-depleted even/odd coherent states in the Fock representation. The results show that photon-added and photon-depleted even/odd coherent states show the desired non-classical characters.
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