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I saw the following talk the other day: http://www.youtube.com/watch?v=dEaecUuEqfc&feature=share

In it, Dr. Ron Garret posits that entanglement isn't really that "special" of a property. He argues (and shows) that the mathematics behind it is analogous to the math behind measurement.

Is this true? There seems to be a lot of hoopla around quantum entanglement (including people that argue it could facilitate faster-than-light (FTL) communication). Is this excitement about the entanglement properties of some elementary particles unwarranted? Just looking for some clarification.

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2 Answers 2

Quantum entanglement and measurement are different point of views of the same underlying physical phenomena, say, the most distinct feature of the evolution of coupling between two physical systems.

From an external point of view, when two physical systems interact, they become entangled. This apply even if one of the systems is large and semi-classical (say, a photon detector). Regardless of the scale of the systems, when there is an interaction, the total system keeps evolving under an unitary propagator, which respects time symmetry.

From the point of view of each system, the coupling does not seem unitary at all; it seems like the other system suddenly collapsed to a random eigenstate of the coupling perturbation. Part of the quantum information that existed in the other eigenstates disapeared and became physically inaccessible. This is how we perceive measurement.

Regrettably, quantum entanglement cannot, by itself, allow FTL communication. The reason is that it produces correlation between measurements far away, but you still are unable to pick which definite state of the entangled superposition will the particles be.

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Regarding your last paragraph: that is not the method by which the author posits FTL communication. Not by picking the state the superposition will collapse to, but by turning on or off the superposition itself. I asked a related question (physics.stackexchange.com/questions/55028/…) to which I never got a satisfactory answer, if you care to take a crack at it. –  user1247 Mar 30 '13 at 19:28
hi user1247, Lubos answers are never satisfactory, but they are correct in the huge majority of cases :-) the problem is exactly what he said in his last paragraph: entanglement superposition is never seen locally; local measurements look as random as random gets. If you don't compare those local measurements with the measurements in the entangled pair, you'll never be able to notice that there was entanglement. Hence there is nothing that you can do remotely that will change the statistical distribution of remote events: all those events look correlated when compared with the remote measureme –  lurscher Mar 31 '13 at 4:16
Thanks. Do you know why entanglement superposition is never seen locally? I'm very confused about this point, because how then, for example, can we ever see interference effects? Isn't each photon we see interfering in the usual double slit experiment ultimately entangled with some other photon or electron in the past? –  user1247 Mar 31 '13 at 9:19

It is difficult to say what it would mean for entanglement to be "the same as measurement", given that entanglement is essentially the phenomenon of the measurement outcomes of two systems being apparently random, but correlated to each other, in more than one basis of measurement. (Entanglement does exist as a concept independently of the measurement process — a pure state of two systems is entangled if and only if it does not factor as a tensor product, for example — but the "physical" significance of this is that the observables on the two factors will have correlated expectation values.) To quote a reasonably well-worded paragraph from the introduction to the Wikipedia article on entanglement:

Quantum entanglement is a form of quantum superposition. When a measurement is made and it causes one member of such a pair to take on a definite value (e.g., clockwise spin), the other member of this entangled pair will at any subsequent time be found to have taken the appropriately correlated value (e.g., counterclockwise spin). Thus, there is a correlation between the results of measurements performed on entangled pairs, and this correlation is observed even though the entangled pair may have been separated by arbitrarily large distances.

Regardless of the reason for this correlation of measurement outcomes, what characterizes entanglement as distinct from "classical randomness" is precisely that the measurement outcomes are correlated in a way which is not straightforwardly explainable in terms of local hidden variables, unless your theory of particle behaviour allows faster-than-light signalling between particles. The "hoopla" comes from attempts to reconcile this in a way that we can picture in terms of classical probabilities, or from explicit rejections of the possibility that we can find such a reconciliation.

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