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Two-mode entangled state is an important quantum resource for quantum information. In this paper, the amplification of a single mode of two-mode entangled state (single-mode amplification scheme) and two modes of two-mode entangled state (two-mode amplification scheme) are theoretically proposed. Here, the optical beam splitter model is used to simulate the vacuum noise introduced by the loss in the optical transmission process. By utilizing the positivity under partial transpose criterion, we analyze the effect of the gain of the four-wave mixing process on the entanglement degree of the initial two-mode entangled state in two different amplification schemes. In these two schemes, we set the gain of the initial two-mode entangled state generation process to be 1.5, 2.5 and 50.0 respectively, and then change the gain of the amplification process in a certain range. We also set the transmission efficiency of the amplified beams for each of the two schemes to be a definite value. The results show that the entanglement of the initial two-mode entangled state decreases with the gain increasing under the condition of specific transmission loss in two schemes. When the gain does not exceed a certain value, the entanglement of the initial two-mode entangled state can be maintained. Then, with the increase of the gain, the entanglement of the initial two-mode entangled state will disappear. Moreover, the entanglement of the initial two-mode entangled state of the two-mode amplification scheme disappears faster than that of the single-mode amplification scheme. Our theoretical results pave the way for the experimental realization of the amplification of two-mode entangled state based on four-wave mixing process.

Amplification of entangled beam based on four-wave mixing process