Editing Quantum teleportation (section)

=== Quantum teleportation over 143 km ===

Zeilinger's group developed an experiment using active feed-forward in real time and two free-space optical links, quantum and classical, between the Canary Islands of La Palma and Tenerife, a distance of over 143 kilometers. The results were published in 2012. In order to achieve teleportation, a frequency-uncorrelated polarization-entangled photon pair source, ultra-low-noise single-photon detectors and entanglement assisted clock synchronization were implemented. The two locations were entangled to share the auxiliary state:<ref name="Ma-2012" />

:<math>|\Psi^-\rangle_{23}=\frac{1}{\surd2}((|H\rangle_2|V\rangle_3)-(|V\rangle_2|H\rangle_3))</math>

La Palma and Tenerife can be compared to the quantum characters Alice and Bob. Alice and Bob share the entangled state above, with photon 2 being with Alice and photon 3 being with Bob. A third party, Charlie, provides photon 1 (the input photon) which will be teleported to Alice in the generalized polarization state:

:<math>|\phi\rangle_1=\alpha|H\rangle_1+\beta|V\rangle_1</math>

where the complex numbers <math>\alpha</math> and <math>\beta</math> are unknown to Alice or Bob.

Alice will perform a Bell-state measurement (BSM) that randomly projects the two photons onto one of the four Bell states with each one having a probability of 25%. Photon 3 will be projected onto <math>|\phi\rangle</math>, the input state. Alice transmits the outcome of the BSM to Bob, via the classical channel, where Bob is able to apply the corresponding unitary operation to obtain photon 3 in the initial state of photon 1. Bob will not have to do anything if he detects the <math>|\psi^-\rangle_{12}</math> state. Bob will need to apply a <math>\pi</math> phase shift to photon 3 between the horizontal and vertical component if the <math>|\psi^+\rangle_{12}</math> state is detected.<ref name="Ma-2012" />

The results of Zeilinger's group concluded that the average fidelity (overlap of the ideal teleported state with the measured density matrix) was 0.863 with a standard deviation of 0.038. The link attenuation during their experiments varied between 28.1&nbsp;dB and 39.0&nbsp;dB, which was a result of strong winds and rapid temperature changes. Despite the high loss in the quantum free-space channel, the average fidelity surpassed the classical limit of 2/3. Therefore, Zeilinger's group successfully demonstrated quantum teleportation over a distance of 143&nbsp;km.<ref name="Ma-2012" />