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Laguerre-polynomial-weighted squeezed vacuum: generation and its properties of entanglement

We theoretically prepare a kind of two-mode entangled non-Gaussian state generated by combining quantum catalysis and parametric-down amplifier operated on the two-mode squeezing vacuum state. We then investigate the entanglement properties by examining Von Neumann entropy, EPR correlation, squeezing effect and the fidelity of teleportation. It is shown that only Von Neumann entropy can be enhanced by both single- and two-mode catalysis in a small squeezing region, while the other properties can be enhanced only by two-mode catalysis including symmetrical and asymmetrical cases. A comparison among these properties shows that the squeezing and the EPR correlation definitely lead to the improvement of both the entanglement and the fidelity, and the region of enhanced fidelity can be seen as a sub-region of the enhanced entanglement which indicates that the entanglement is not always beneficial for the fidelity. In addition, the effect of photon-loss after catalysis on the fidelity is considered and the symmetrical two-photon catalysis may present better behavior than the symmetrical single-photon case against the decoherence in a certain region.