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Chinese Physics

Entanglement swapping of continuous variable using squeezed vacuum states

Wei Ping Yan, Zhang Wei-Jun

Published Oct 1, 2007• 1 citation
Publisher

Abstract

We present a realistic scheme for the entanglement swapping of continuous variable, in which a two-mode squeezed vacuum state serves as a quantum channel. The position sum and momentum difference of two local modes are measured. By taking the input entangled state also as a two-mode squeezed vacuum state, we investigate the average fidelity and the von Neumann entropy of the output state. The results show that the perfect teleportation can be achieved by increasing the squeezing of the quantum channel and that any nonzero squeezing in both the quantum channel and the input entangled state is sufficient to swap the entanglement.

DOI
10.1088/1009-1963/16/10/010

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We present a realistic scheme for the entanglement swapping of continuous variable, in which a two-mode squeezed vacuum state serves as a quantum channel. The position sum and momentum difference of two local modes are measured. By taking the input entangled state also as a two-mode squeezed vacuum state, we investigate the average fidelity and the von Neumann entropy of the output state. The results show that the perfect teleportation can be achieved by increasing the squeezing of the quantum channel and that any nonzero squeezing in both the quantum channel and the input entangled state is sufficient to swap the entanglement.
We investigate the entanglement swapping of the continuous variable states by taking the pair Schrödinger cat states as the input entangled states, in which the two-mode squeezed vacuum and the pair cat states serve as the quantum channel, respectively. The entanglement of the initial states as well as the final states is analyzed by adopting the logarithmic negativity as the measure of entanglement. The quantum teleportation task by exploiting the swapped states as the quantum channel is also considered, where a coherent state serves as the target state and the average fidelity is examined.
Entanglement swapping of two-mode Gaussian states is investigated by use of quantum teleportation protocol of continuous variables. In the entanglement swapping protocol, we take the two-mode squeezed vacuum which is exposed in a thermal environment as a mixed-quantum-channel state and a two-mode standard form Gaussian state as an input state to be teleported. When the input state is pure, we find that the swapped state is inseparable if and only if both the input state and the quantum-channel state are entangled. When the input state is mixed and entangled, we find that the swapped state is inseparable only if the quantum-channel state is sufficiently much entangled. We also notice that the required minimum entanglement in the mixed quantum channel to maintain entanglement in the swapped state strongly depends on the global purity of the input state.
The teleportation of two-mode continuous variables was performed by using two two-mode squeezed vacuum states served as quantum channel.The average fidelity and the probability density were calculated for teleportation of a two-mode squeezed vacuum state.The results indicate that increased squeezing of teleported state will lead to a loss of fidelity.The probability density of measuring result consists of the product of two bivariate normed density functions,and it shows that when the average fidelity goes up,the probability of obtaining large measurement value also increases.
This paper presents a realistic scheme for the teleportation of coherent states in which a two-mode squeezed vacuum state serves as the quantum channel and the position-sum and momentum-difference of two local modes serve as the measuring observables. The average fidelity of the teleportation of coherent states is derived for finite squeezing parameters and it turns out that fidelity greater than ½ cannot be achieved by using a classical channel alone and the probability distribution of the measurement result is a Gaussian distribution around the unknown parameter of the input coherent state with a width given by the squeezing parameter.
We investigate the entanglement swapping of non-Gaussian states, including squeezed number states, two-mode photon-added states, and two-mode photon-subtracted squeezed states and analyze the entanglement of the swapped states by adopting logarithmic negativity as the measure of entanglement. Furthermore, we examine the fidelity of teleportation protocols for different input states where the swapped states serve as the quantum channel. All these results are compared with that obtained in the case of Gaussian two-mode squeezed vacuum.