Does the entanglement happen between two particles or two wavefunctions? If it's wavefunction then what happens to the two wavefuntions after getting entangled?
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Any physical system has a wavefunction that describes the whole system. So even when we have two particles that are not entangled the two of them are described by some single wavefunction $\Psi$. However when we say the particles are not entangled we mean the total wavefunction can be separated into different parts for each particle. So we can write:
$$ \Psi = \psi_a \psi_b \tag{1} $$
where $\psi_a$ describes just particle $A$ and $\psi_b$ describes just particle $B$. For convenience we often refer to $\psi_a$ as the wavefunction of particle $A$, and likewise for $B$, but strictly speaking $\psi_a$ and $\psi_b$ are just parts of the wavefunction for the system.
When the two particles become entangled the means the total wavefunction $\Psi$ can no longer be separated into an $A$ part and a $B$ part, so we can no longer write down an equation like equation (1). In effect the two particles have become mixed up and can no longer be distinguished from each other.
John Rennie
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Does the collapse of the wavefunction describing spin entangled particles A & B result in two definite states A & B or single state containing destroyed entanglement of particles A & B? – Viswa Vijeta Feb 24 '19 at 16:45
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@ViswaVijeta exactly how the collapse occurs is not known. There are competing theories, of which my favourite involves a process called decoherence. The end result of this will be a separable wavefunction like my equation (1). – John Rennie Feb 24 '19 at 16:57
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Is decoherence environmental entanglement? Is it many world interpretation you're talking about? – Viswa Vijeta Feb 24 '19 at 17:17
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When two particles have quantum entanglement, they have a common wavefunction.
The wavefunction is the probability distribution of the particles' position in all of space.
When the two particles are entangled, they common wavefunction describes both of their properties.
That is why as long as the entanglement is there, they can be described by one single wavefunction, and if you check the properties of one particle, you will have checked the common wavefunction, what is the wavefunction of the other particle too. that is why you have affected the properties of the other particle too.
It is a common misconception that at the moment of checking the common wavefunction, you collapse it. Nothing is collapsing. You just affect the common wavefunction itself by checking it, so it will have an effect on the other particle's properties too.
Árpád Szendrei
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What do you mean by "affecting the common wavefunction? Isn't affecting same as collapsing? – Viswa Vijeta Feb 23 '19 at 17:06
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And doesn't the entanglement break the moment we check the common wavefunction? And now both particles are described by separate wavefunction, if yes then why wavefunction got separated the moment we check it? – Viswa Vijeta Feb 23 '19 at 17:13
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Yes, people commonly use the word collapsing, but it is just when certain properties of the particle are revealed, The wavefunction describes the probability distribution for all of space. When you check the properties of the particle, basically, you will reveal, for a certain property, the actual value. That value will be then certain. But by doing so, all the other properties of it will be uncertain, and if both particles have the same wavefunction, the other particle's other (the one's you did not check for the first particle) properties will be uncertain. – Árpád Szendrei Feb 23 '19 at 22:22
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No, when you check the first particle, the entanglement will not (not in all cases) be destroyed. Otherwise how could you check if they were entangled? – Árpád Szendrei Feb 23 '19 at 22:22