Thursday, May 14, 2009

Quantum teleportation along a quantum spin chain

My son, Luke is doing a school project (year 10 science issues) on teleportation. He picked the topic! When discussing it with him I found this nice visualization and explanation on Youtube.
I think I first "understood" quantum teleportation when I worked on a project with John Paul Barjaktarevic, Jon Links, and Gerard Milburn. We were trying to answer two questions:
How does one quantify the amount of quantum entanglement in the ground state of a quantum many-body system?

How can one use that entanglement as a resource to perform quantum information processing, e.g., tasks such as teleoportation?
We considered the ground state of a Heisenberg antiferrromagnetic spin 1/2 chain. John Paul found numerically a result that I found surprising: if one makes a series of projective measurements of the spin state of pairs of spins along the chain one can teleport with perfect fidelity the state of a free spin at the left end of the chain to the right end of the chain. Given that the spin correlations decay (as a power law) with distance I expected that the fidelity would decay with the length of the chain. We then came up with an argument based on valence bond theory which enabled us to justify the result for any singlet state. We talked to Jon Links who produced a very elegant group theoretic argument which proved the result held in general. The relevant papers are here and here.

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