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arXiv:quant-ph/9807069 · Physical Review A

Bound entanglement and teleportation

Noah Linden, Sandu Popescu

Published Jan 1, 1999• 31 citations
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Abstract

Recently M. Horodecki, P. Horodecki, and R. Horodecki [Phys. Rev. Lett. 80, 5239 (1998)] have introduced a set of density matrices of two spin-1 particles from which it is not possible to distill any maximally entangled states, even though the density matrices are entangled. Thus these density matrices do not allow reliable teleportation. However, it might nevertheless be the case that these states can be used for teleportation, not reliably, but still with fidelity greater than that which may be achieved with a classical scheme. We show that, at least for some of these density matrices, teleportation cannot be achieved with better than classical fidelity.

DOI
10.1103/physreva.59.137

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Recently M. Horodecki, P. Horodecki, and R. Horodecki [Phys. Rev. Lett. 80, 5239 (1998)] have introduced a set of density matrices of two spin-1 particles from which it is not possible to distill any maximally entangled states, even though the density matrices are entangled. Thus these density matrices do not allow reliable teleportation. However, it might nevertheless be the case that these states can be used for teleportation, not reliably, but still with fidelity greater than that which may be achieved with a classical scheme. We show that, at least for some of these density matrices, teleportation cannot be achieved with better than classical fidelity.
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 (Nature 390,575 (1997)) 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 (Phys. Rev. Lett. 80, 3891 (1998)), 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 up to date that demonstrates the teleportation of a genuine unknown quantum state. 1
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.
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.