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arXiv:quant-ph/0204011 · Physical Review A

Continuous-variable quantum teleportation of entanglement

Tyler J. Johnson, Stephen D. Bartlett, Barry C. Sanders

Published Oct 30, 2002• 40 citations
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Abstract

Entangled coherent states can be used to determine the entanglement fidelity for a device that is designed to teleport coherent states. This entanglement fidelity is universal in that the calculation is independent of the use of entangled coherent states and applies generally to the teleportation of entanglement using coherent states. The average fidelity is shown to be a poor indicator of the capability of teleporting entanglement; i.e., very high average fidelity for the quantum teleportation apparatus can still result in low entanglement fidelity for one-mode of the two-mode entangled coherent states.

DOI
10.1103/physreva.66.042326

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Entangled coherent states can be used to determine the entanglement fidelity for a device that is designed to teleport coherent states. This entanglement fidelity is universal in that the calculation is independent of the use of entangled coherent states and applies generally to the teleportation of entanglement using coherent states. The average fidelity is shown to be a poor indicator of the capability of teleporting entanglement; i.e., very high average fidelity for the quantum teleportation apparatus can still result in low entanglement fidelity for one-mode of the two-mode entangled coherent states.
We experimentally demonstrate quantum teleportation for continuous variables using squeezed-state entanglement. The teleportation fidelity for a real experimental system is calculated explicitly, including relevant imperfection factors such as propagation losses, detection inefficiencies, and phase fluctuations. The inferred fidelity for input coherent states is $F=0.61\ifmmode\pm\else\textpm\fi{}0.02,$ which when corrected for the efficiency of detection by the output observer, gives a fidelity of 0.62.0.62.0.62. By contrast, the projected result based on the independently measured entanglement and efficiencies is 0.69.0.69.0.69. The teleportation protocol is explained in detail, including a discussion on discrepancy between experiment and theory, as well as on the limitations of the current apparatus.
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 entanglement states in continuous-variable quantum teleportation can transfer any quantum state. However, errors occur in the quantum states before and after the transfer in scientific experiments because generating a perfect quantum entanglement is physically unattainable. This paper limits the quantum states transferred to squeezed coherent states and introduces a controller to classical information transfer in continuous-variable quantum teleportation to improve transfer accuracy. Under such a setup, we derived the optimal controller that maximizes the fidelity, independent of the measurement results and the value of the displacement of the squeezed coherent state.