Trivial quantum entanglement question (from a rookie)

[DanteKennedy]

TL;DR

How quantum entanglement works? Can more than two particles became entangled together? Is it possible to predict the condition of the entire entangled system if we measure only a part of it? Are my questions even make sense?

Based on my surface level knowledge, one example of quantum entanglement are the electron spins, where if we observed one of the entangled electron, the outcome will appear for both electrons. But what I'm curious is that is the outcome of the other entangled electron already "pre determined?" If that makes sense? (ex. if observed spin-up, then other must spin-down) Or is the outcome still "random" and entanglement is like just "forcing" entangled particles to have definite result? Sorry for the terrible explanation, but I will try my best to clarify what I mean if anyone ask

 

[PeroK]

You have several misconceptions about entanglement.

First, entanglement is often a result of conservation laws and any number of particles or subsystems can be entangled. For example, if you know the total energy of a system and you measure the energy of part of the system, then you know the energy of the remaining part(s). This is the case for both classical physics and QM.

The difference is that the value of dynamic properties like position, momentum, angular momentum and energy are not well-defined in QM until a measurement is made. In a classical system, each component has a definite well-defined position, momentum, angular momentum and energy at all times. If you measure the energy of one component, then you are simply recording a value of energy that the component already had. And the other components inevitably have values in accordance with the conservation laws.

With QM, the state of a component is often a superposition of different position, momentum, angular momentum and/or energy. The trick that QM pulls is to correlate different measurements on an entangled system so that the conservation laws are maintained. On the face of it, this seems impossible. But, experiments show that this is indeed the case. Through entanglement, QM correlates measurements in ways that are quite literally impossible in classical physics.

Moreover, in QM we should really talk about a system being in an entangled state - rather than individual particles being entangled with each other. In the case of the spins of two electrons, we really have an entangled system of two electrons. The electrons cannot be described each by its own quantum state.

From that point of view, a measurement of one of the electrons is a measurement of the whole system. The system then collapses into an unentangled state (this is the orthodox interpretation), determining the spin of the both particles (about the measured axis).

I suggest you read much more thoroughly about QM. A lot of your questions about entanglement are probably questions about QM generally. You need to fundamentally understand what QM is saying before you can start to think about quantum entanglement.