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Journal of the Korean Physical Society

Quantum teleportation via mixed two-mode squeezed states in the coherent-state representation

Jinhyoung Lee, M. S. Kim, S. Lee

Published Apr 1, 2003• 1 citation
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Abstract

Quantum teleportation for continuous variables is generally described in phase space by using the Wigner functions. We study quantum teleportation via a mixed two-mode squeezed state in Hilbert-Schmidt space by using the coherent-state representation and operators. This shows directly how the teleported state is related to the original state. PACS numbers: 03.67.-a, 89.70.+c

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Quantum teleportation for continuous variables is generally described in phase space by using the Wigner functions. We study quantum teleportation via a mixed two-mode squeezed state in Hilbert-Schmidt space by using the coherent-state representation and operators. This shows directly how the teleported state is related to the original state. PACS numbers: 03.67.-a, 89.70.+c
The phase-space method is applied for considering continuous variable quantum teleportation. It is found that the continuous variable quantum teleportation transforms the sss-parametrized phase-space function of an input state into the $(s+\ensuremath{\delta})$-parametrized phase-space function, where the parameter $\ensuremath{\delta}$ is determined by the shared quantum entanglement. It is shown from this result that the Wigner function of the teleported state is always non-negative for ${\mathcal{F}}_{c}\ensuremath{\leqslant}2∕3$ and the Glauber-Sudarshan PPP function non-negative for ${\mathcal{F}}_{c}\ensuremath{\leqslant}1∕2$, where Fc{\mathcal{F}}_{c}Fc​ is the fidelity of the coherent-state teleportation. Furthermore the fidelity between input and output states is calculated when Gaussian states are teleported.
Quantum teleportation of a continuous-variable state is studied for the quantum channel of a two-mode squeezed vacuum influenced by a thermal environment. Each mode of the squeezed vacuum is assumed to undergo the same thermal influence. It is found that when the mixed two-mode squeezed vacuum for the quantum channel is separable, any nonclassical features, which may be imposed in an original unknown state, cannot be transferred to a receiving station. A two-mode Gaussian state, one of which is a mixed two-mode squeezed vacuum, is separable if and only if a positive well-defined P function can be assigned to it. The fidelity of teleportation is considered in terms of the noise factor given by the imperfect channel. It is found that quantum teleportation may give more noise than direct transmission of a field under the thermal environment, which is due to the fragile nature of quantum entanglement of the quantum channel.