Entanglement Improvement of Three-mode Squeezed Vacuum State Via Number-conserving Operation

In this paper, the quantum entanglement properties of a three-mode squeezed vacuum state under an ideal and realistic scenario are discussed. We find that photon loss has a significant negative effect on quantum entanglement, leading to the degradation of entangled states and the loss of fidelity. In order to overcome this challenge, we further study the effect of number-conserving operation on the entangled properties of three-mode squeezed vacuum states. In general, when the squeezing amplitude is small, the multi-mode and high-order number-conserving operation has the optimal effect on the improvement of entanglement. With the increase of squeezing amplitude, we need to reduce the number of operated modes and the order of number-conserving operation to obtain the optimal improvement effect. When the squeezing amplitude is large enough, the number-conserving operation no longer has the improvement effect. The results in this paper are helpful to further understand the multi-mode squeezed vacuum state and provide an estimable theoretical basis for its application in quantum information processing.