ZapperZ said:
I don't know either, mainly because I've yet to be presented with compelling evidence of such "irreversible entanglement".
The point is that there are TWO ways to explain *conceptually* the *same* observational phenomena. One way is to say that "entanglement stops", which can be interpreted as saying that we switch to a statistical mixture of product state description, which can then in a second step be re-interpreted as a classical description (there's still a distinction between both, in that individual subsystems can still be in non-classical states, but the entanglement between subsystems seems to be gone: we have a product state). The observable consequence of this is that one cannot obtain any quantum interference effects in the CORRELATIONS between observations on the different subsystems.
But the other way is to say that the "entanglement is now irreversibly enlarged with the environment". Well, the observable consequence of this is ALSO that one will not obtain any quantum interference effects anymore in the CORRELATIONS between observations of ONLY the two subsystems (and not of the miriads of "subsystems" of the environment).
In other words "everything entangled" and "end of entanglemetn" are observationally equivalent. They are just two conceptually different ways of thinking about how things behave. They are FAPP observationally indistinguishable. So asking for *experimental proof* for one or the other is an impossible request.
One shouldn't confuse "entanglement" with "quantum interference effects". In fact, entanglement SUPPRESSES low-order interference effects, to show them in higher-order correlations. And with irreversible entanglement with the environment, that means then that the ONLY potentially observable quantum interference effects will happen in the n-point correlation functions with n very large, meaning: impossible to observe. We can't observe 10^20-point correlation functions.
How does this come about ?
Let's look at a toy example:
We have 5 quantum systems in our toy world: S1, S2, S3, S4, and S5.
Let us assume that we prepared system S1 in a non-classical state (a superposition of "classical" states |S1A> and |S1B>).
Our "universe state" is now:
{ |S1A> - |S1B> } |S2X> |S3Y> |S4Z> |S5U>
It is a product state, in which we can consider the 5 systems independently. But, by JUST doing a measurement on system S1, we can find quantum interference, if somehow we find a measurement setup that measures |S1A> + |S1B> versus |S1A> - |S1B>.
Indeed, "classically" we would expect this to be 50% 50% (if we assumed that the system was a 50% / 50% mixture of S1A and S1B). And we will find 0% and 100%. That DEVIATION from the statistical mixture is a quantum interference phenomenon. It is the fingerprint of quantum effects.
Assume now that system S1 interacts with system S2.
We now have the universe state:
{ |S1A> |S2A> - |S1B>|S2B> } |S3Y> |S4Z> |S5U>
Well, if we NOW do the mesurement on S1 with the |S1A> + |S1B> versus |S1A> - |S1B> measurement device, we will find: 50% and 50%. The quantum signature 100% - 0% is gone. The system S1, BY ITSELF, doesn't seem to show ahy quantum behaviour anymore.
However, if we do a quantum CORRELATION experiment between system S1 and S2, and we check for "AA" versus "BB" results, we will find 50% AA, 50% BB, 0% AB and 0% BA. That still corresponds to a mixture, but if we start doing Bell-type experiments on the double system S1 and S2, we WILL find quantum interference effects, which show up here as violations of Bell's inequalities for instance. Or simpler: a measurement on the state:
{ ( |S1A> - |S1B> ) (|S2A> - |S2B> ) - ( |S1A> + |S1B> ) (|S2A> + |S2B> ) }
= - 2 |S1A> |S2B> - 2 |S1B> |S2A>
would yield 0 while we would expect, if we would have a statistical mixture: 25% (one should normalize the states).
This deviation from the statistical mixture prediction indicates a quantum effect, but notice that now, it only appears in 2-point correlation functions (between S1 and S2). It doesn't appear anymore in any measurement that you can do on S1 alone, or on S2 alone.
Now, let us suppose that we have the 5 systems entangled:
|S1A>|S2A>|S3A>|S4A>|S5A> - |S1A>|S2A>|S3A>|S4A>|S5A>
It takes more algebra, but you can find out that you will not find any deviation from any measurement that only takes into account 1, 2, 3 or 4 of these 5 systems. Each of these individual measurements, or 2-point correlations, or 3-point correlations (say, between S1, S2 and S3), or 4-point correlations (say, between S1,S2,S3 and S4) will be indistinguishable from the "mixture" case. BUT there will now be an observable interference effect in the 5-point correlation function (the measurement on |S1A>|S2A>|S3A>|S4A>|S5A> + |S1A>|S2A>|S3A>|S4A>|S5A> will yield zero, while we expect it to be 50%)
As our toy universe doesn't have more than 5 subsystems, 5-point correlation functions describe every thinkable experimental outcome. So "entanglement forever" will be equivalent to "no entanglement anymore" for 1, 2, 3 and 4-point correlation functions, but for 5-point correlation functions, we WILL see the difference.
In our universe however, there are many many more subsystems.