Quantum Information Theory with Gaussian Systems

3.6 Teleportation criteria
carry the best approximation to the input state since there can be no better clone
in any other subsystem. This constitutes the second type of success criterion for
continuous-variable teleportation:
Corollary 3.13:
If the fidelity of a teleported coherent state with respect to the original input state
exceeds a value of f ≈ 0.6826, the output system is the best remaining clone of
the input state.
Of course, by Corollary 3.12, this teleportation process must have been assisted by
non-ppt entanglement. A similar result has been obtained in [65]; while it is based
on the same argument, it considers only the best Gaussian cloner with fidelity 2
3 .
Until recently, experimental teleportation of coherent states reached fidelities just
below 2
3 , the fidelity of the best Gaussian 1-to-2 cloner. For example, the seminal
experiment of Furusawa et al. [66] yielded fidelities of 0.58 ± 0.02. Later, Bowen
et al. [67] reached fidelities of 0.64 ± 0.02 and Zhang et al. [68] reported fidelities
of 0.61 ± 0.02. Only recently, Furusawa et al. [69] achieved a fidelity of 0.70 ± 0.02,
surpassing both the Gaussian and the optimal limit.
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