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Journal of Optics B Quantum and Semiclassical Optics

Wigner function description of continuous variable entanglement swapping

Jin‐Ming Liu, Bao‐Sen Shi, Xiao-Feng Fan, Jian Li, Guang‐Can Guo

Published Jun 18, 2001• 13 citations
Publisher

Abstract

We discuss the continuous variable entanglement swapping using the Wigner function. The sufficient inseparability criterion for continuous variable systems is used to analyse the quantum correlation. Perfect teleportation can be obtained by increasing the degree of squeezing on the entanglement source. Entanglement swapping occurs for any nonzero squeezing in both of the two initial sources if optimal gain is obtained.

DOI
10.1088/1464-4266/3/4/301

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We discuss the continuous variable entanglement swapping using the Wigner function. The sufficient inseparability criterion for continuous variable systems is used to analyse the quantum correlation. Perfect teleportation can be obtained by increasing the degree of squeezing on the entanglement source. Entanglement swapping occurs for any nonzero squeezing in both of the two initial sources if optimal gain is obtained.
With the application of a Wigner function description of a two-mode squeezed state,we study a protocol of continuous variable entanglement swapping in a noisy quantum channel.Assuming that the two initial entangled states are coupled with the same environment,we analyse the quantum state emerging from the swapping and obtain the inseparable condition for the output correlation.It is found that there is more noise resulting from the entanglement swapping than from the direct transmission,no matter what values of displacement gain are chosen.
With the application of a Wigner function description of a two-mode squeezed state, we study a protocol of continuous variable entanglement swapping in a noisy quantum channel. Assuming that the two initial entangled states are coupled with the same environment, we analyse the quantum state emerging from the swapping and obtain the inseparable condition for the output correlation. It is found that there is more noise resulting from the entanglement swapping than from the direct transmission, no matter what values of displacement gain are chosen.
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.
Teleportation is a basic primitive for quantum communication and quantum computing. We address the problem of continuous-variable (unconditional and conditional) teleportation of a pure single-photon state and a mixed attenuated single-photon state generally in a nonunity-gain regime. Our figure of merit is the maximum negativity of the Wigner function, which demonstrates a highly nonclassical feature of the teleported state. We find that the negativity of the Wigner function of the single-photon state can be unconditionally teleported for an arbitrarily weak squeezed state used to create the entangled state shared in teleportation. In contrast, for the attenuated single-photon state there is a strict threshold squeezing one has to surpass to successfully teleport the negativity of its Wigner function. The conditional teleportation allows one to approach perfect transmission of the single photon for an arbitrarily low squeezing at a cost of decrease of the success rate. In contrast, for the attenuated single photon state, conditional teleportation cannot overcome the squeezing threshold of the unconditional teleportation and it approaches negativity of the input state only if the squeezing increases simultaneously. However, as soon as the threshold squeezing is surpassed, conditional teleportation still pronouncedly outperforms the unconditional one. The main consequences for quantum communication and quantum computing with continuous variables are discussed.
We investigate the efficacy with which polarization entanglement can be teleported using a continuous measurement scheme. We show that by using the correct gain for the classical channel the degree of violation of locality that can be demonstrated (using a CH-type inequality) is not a function of the level of entanglement squeezing used in the teleportation. This is possible because a gain condition can always be chosen such that passage through the teleporter is equivalent to pure attenuation of the input field.