Quantaportation

A while back the New York Times reported an experiment that managed to “teleport” the information from one atom into another over a distance of about a meter. It’s a fun read:

http://www.nytimes.com/2009/02/03/science/03teleportation.html?_r=1&ref=science

Quantum teleportation rests on the ability for quantum particles to become “entangled”. The basic idea here is that the state of a system of quantum particles does not always break down neatly into a sum of states of the individual particles. The total state is “bigger” than the sum of the parts.

This “not the sum of its parts” business is evident from some of the simplest quantum experiments one can do. The famous double-slit experiment rests on the fact that if you fire a beam of electrons at a screen that has two slits cut out of it (a very short distance apart from one another), then after the beam hits the slit, each particle in the beam is described by a wavefunction that involves two pieces:

(Psi_1 + Psi_2)/(sqrt(2))

where the first piece corresponds to passing through slit 1while the second piece corresponds to passing through slit 2

The probability distribution for a particle in the beam is the square of the above:

[(Psi_1)^2 + (Psi_2)^2 + 2 Psi_1 Psi_2]/2

The last term in the square-brackets would not come about if these electrons behaved like classical particles. There would simply be a 50% chance of the particles passing through slit 1 and 50% chance that they passed through slit 2. That last term has the effect of creating an interference pattern as the electrons hit some photographic plate beyond the double-slits.

Entanglement works on a similar principle, only now, rather than a single particle, a *single* wavefunction necessarily describes the state of the two particles. This wavefunction is set up in some way to ensure that some constraint is met–if the particles were photons that arose from the decay of a particle with zero angular momentum, then the total angular momentum for the photons is zero. This means that if you measure the spin of your photon, you know the spin of your friend’s photon.

The crazy thing is that by *measuring* the photon’s spin, you appear to have an influence on the spin of your friend’s photon. This influence appears to act instantaneously. This is what makes entanglement puzzling–it seems to go against Einstein’s special theory of relativity. In fact, it doesn’t because you cannot transmit the information you discover upon your measurement of the photon’s spin to your friend fast enough, and it is information transmission that matters. Still, as a professor I had once said: quantum theory obeys the letter of the law, but seems to certainly skirt close to breaking the spirit…

I guess quantum mechanics is still better than some in the financial industry…

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