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arXiv:0705.2931 · Physical Review A

Sequential quantum teleportation of optical coherent states

Hidehiro Yonezawa, Akira Furusawa, Peter van Loock

Published Sep 6, 2007• 26 citations
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Abstract

We demonstrate a sequence of two quantum teleportations of optical coherent states, combining two high-fidelity teleporters for continuous variables. In our experiment, the individual teleportation fidelities are evaluated as ${F}_{1}=0.70\ifmmode\pm\else\textpm\fi{}0.02$ and ${F}_{2}=0.75\ifmmode\pm\else\textpm\fi{}0.02$, while the fidelity between the input and the sequentially teleported states is determined as ${F}^{(2)}=0.57\ifmmode\pm\else\textpm\fi{}0.02$. This still exceeds the optimal fidelity of one half for classical teleportation of arbitrary coherent states and almost attains the value of the first (unsequential) quantum teleportation experiment with optical coherent states.

DOI
10.1103/physreva.76.032305

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We demonstrate a sequence of two quantum teleportations of optical coherent states, combining two high-fidelity teleporters for continuous variables. In our experiment, the individual teleportation fidelities are evaluated as F1=0.70\ifmmode±\else\textpm\fi0.02{F}_{1}=0.70\ifmmode\pm\else\textpm\fi{}0.02F1​=0.70\ifmmode±\else\textpm\fi0.02 and F2=0.75\ifmmode±\else\textpm\fi0.02{F}_{2}=0.75\ifmmode\pm\else\textpm\fi{}0.02F2​=0.75\ifmmode±\else\textpm\fi0.02, while the fidelity between the input and the sequentially teleported states is determined as F(2)=0.57\ifmmode±\else\textpm\fi0.02{F}^{(2)}=0.57\ifmmode\pm\else\textpm\fi{}0.02F(2)=0.57\ifmmode±\else\textpm\fi0.02. This still exceeds the optimal fidelity of one half for classical teleportation of arbitrary coherent states and almost attains the value of the first (unsequential) quantum teleportation experiment with optical coherent states.
The progress in quantum operations of continuous-variable (CV) schemes can be reduced to that in CV quantum teleportation. The fidelity of quantum teleportation of an optical setup is limited by the finite degree of quantum correlation that can be prepared with a pair of finitely squeezed states. Reports of improvement of squeezing level have appeared recently, and we adopted the improved methods in our experimental system of quantum teleportation. As a result, we teleported a coherent state with a fidelity $F=0.83\ifmmode\pm\else\textpm\fi{}0.01$, which is better than any other figures reported to date, to our knowledge. In this paper, we introduce a measure ns{n}_{s}ns​, the number of teleportations expected to be carried out sequentially. Our result corresponds to ${n}_{s}=5.0\ifmmode\pm\else\textpm\fi{}0.4$. It suggests that our improvement would enable us to proceed toward more advanced quantum operations involving multiple steps.
We derive an experimentally testable criterion for the teleportation of quantum states of continuous variables. This criterion is especially relevant to the recent experiment of Furusawa et al. [Science 282, 706-709 (1998)] where an input-output fidelity of 0.58pm0.020.58 \\pm 0.020.58pm0.02 was achieved for optical coherent states. Our derivation demonstrates that fidelities greater than 1/2 could not have been achieved through the use of a classical channel alone; quantum entanglement was a crucial ingredient in the experiment.
Quantum teleportation is one of the essential primitives of quantum communication. We suggest that any quantum teleportation scheme can be characterized by its efficiency, i.e. how often it succeeds to teleport, its fidelity, i.e. how well the input state is reproduced at the output, and by its insensitivity to cross talk, i.e. how well it rejects an input state that is not intended to teleport. We discuss these criteria for the two teleportation experiments of independent qubits which have been performed thus far. In the first experiment (1997, Nature, 390, 575) where the qubit states were various different polarization states of photons, the fidelity of teleportation was as high as 0.80 ± 0.05 thus clearly surpassing the limit of 2/3 which can, in principle, be obtained by a direct measurement on the qubit and classical communication. This high fidelity is confirmed in our second experiment (1998, Phys. Rev. Lett., 80, 3891), demonstrating entanglement swapping, that is, realizing the teleportation of a qubit which itself is still entangled to another one. This experiment is the only one to date that demonstrates the teleportation of a genuine unknown quantum state.