When does superposition collapse or entanglement take place

[Trollfaz]

When two quantum objects interact, when does this interaction destroy their superposition and when does this interaction causes them to be entangled and allow the superposition to remain.

 

[bhobba]

First I think we need to get some terms straight:

1. QM does not have collapse if that what you are driving at - it's an interpretation thing. Indeed in a recent discussion the science advisers had even what collapse was, was difficult to pin down. The best was its simply the Born Rule which isn't really saying much of anything. So what do you mean by it?

2. Superposition of what? All quantum object's are in superposition all the time. Its like real numbers. 6= 3+3 so 6 is a supposition of 3 and 3. 6 = 4 + 2 so 6 is a superposition of 4 and 2. So you need to be precise about what you mean by it - superposition of momentum, position, energy or what?

If you are talking about decoherence then when systems interact they can become entangled. The exact point they become entangled will depend on the interaction - but its usually pretty quick so pinning it down isn't that easy. Consider two systems each of which can be in state |a> and |b>. They interact in some way and are in state 1/√2 |a>|b> + 1/√2 |b>|a>. They are entangled - but the total system is in the superposition I wrote down (plus tons of others). Now let's just observe one system - say system 1. It not in a pure quantum state because of the entanglement (but see later for the subtlety here) and hence not in a superposition (superposition's only apply to pure states). So we can say its no longer in a superposition once its entangled ie once the interaction that caused the entanglement has taken place. But note; if you observe system 1 it acts as if its in a mixed state 1/2 |a> + 1/2 |b> (you can chug through the math - this is an I level thread so you should be able to do that - if not just take my word for it - I have posted the math in the past). That means there is no way you can tell if its in what is called a proper mixed state or an inproper one. If its a proper one it means then its definitely in state |a> or |b> (remember the subtlety I mentioned before?) with a 50/50 chance. If its inproper it means its described by a mixed state but we do not know if its actually in some state or not - there is no way to tell the difference. FAPP (For All Practical Purposes) the systems state has changed to be either |a> or |b> - that is known as FAPP collapse. Is it actual collapse (assuming of course you can define what actual collapse is) or just a trick of the math. Who knows - and that is the territory of interpretations.

Me, I believe its irrelevant - if its FAPP collapse or some kind of actual collapse (whatever that is) is just quibbling, since there is no way to tell the difference - but from such quibbling long and sometimes heated 'discussions' and differing interpretations are built.

Bottom line is - your question is imprecise the way you asked it, and in giving it precision a lot of subtleties are encountered.

Thanks
Bill

 

[zonde]

When two quantum objects interact, when does this interaction destroy their superposition and when does this interaction causes them to be entangled and allow the superposition to remain.

You can speak about collapse when you consider model that has something to say about single particle events. And this is domain of interpretations.
If you would ask about projection instead of collapse there can be interpretation independent answers.
When different modes end up as different beams after interaction with experimental equipment you can use projection to describe separate beam. But if beams later on overlap you still have to consider whole wavefunction (superposition remains, loosely speaking).

 

[zonde]

2. Superposition of what? All quantum object's are in superposition all the time. Its like real numbers. 6= 3+3 so 6 is a supposition of 3 and 3. 6 = 4 + 2 so 6 is a superposition of 4 and 2.

Extending a bit on bhobba's analogy with numbers.
We can write 6=3+3 or we can write 6=9-3. If we discard information about signs we can not restore original number from the two other numbers i.e. we don't know if 3 and 3 is 6(-6) (3+3 or -3-3) or 0(3-3 or -3+3). So loosely speaking when we discard signs we "destroy superposition".