[Kryptid (OP)]

From what I understand, quantum entanglement means that two or more subatomic particles have certain properties that correlate with one-another despite any distance between them. I have a few questions in regards to this phenomenon:

1) What properties of an entangled pair of particles are correlated?
Are both particles' spins always in the same direction? Always in the opposite direction? Are their momenta correlated? Their direction of motion through space? Anything else?

2) How do we know that a particular pair of particles are entangled with one-another?
I've read that in order to prevent a violation of causality, information cannot be sent instantaneously via a pair of entangled particles. Apparently, if you try to send a signal to particle B by manipulating particle A's properties, the message that anyone looking at particle B will see will be random or garbled. If this is the case, how can we know that particles A and B are even entangled? In order for us to tell that they are entangled, we have to be able to measure that there is a correlation between the two particles' properties in the first place. If particle B's properties seem random when compared to particle A's when measured, then how can we know there is a correlation?

3) How does particle 'splitting' affect entanglement?
If I have two photons A and B that are entangled, and I send A through an extremely powerful magnetic field so that it splits into two weaker photons A1 and A2, will both of these new photons be entangled with photon B? Will only A1 or A2 be entangled with B but not both A1 and A2? Will photon B split as well?

4) Can two dissimilar particles be entangled?
Can a photon be entangled with an electron? Can a quark in a proton be entangled with a quark in a neutron?

*As an add-on, I've read about a hypothesis (or theory) that electrons are actually tiny charged black holes. Perhaps we can say that other subatomic particles are black holes too. Assuming that this is the case, and an unentangled electron is indeed a blackhole, then might two entangled electrons represent the two mouths of a tiny wormhole, thus explaining how one can affect the other through space?

[JP]

1) What properties of an entangled pair of particles are correlated?
Are both particles' spins always in the same direction? Always in the opposite direction? Are their momenta correlated? Their direction of motion through space? Anything else?

Most entanglement that I'm aware of uses photons and spin because photons are easy to generate and handle, and photon spin only has 2 possible values.  However, particles could be entangled through correlations in any measurable quantity: momenta, direction of motion, angular momentum, frequency, etc.

2) How do we know that a particular pair of particles are entangled with one-another?
I've read that in order to prevent a violation of causality, information cannot be sent instantaneously via a pair of entangled particles. Apparently, if you try to send a signal to particle B by manipulating particle A's properties, the message that anyone looking at particle B will see will be random or garbled. If this is the case, how can we know that particles A and B are even entangled? In order for us to tell that they are entangled, we have to be able to measure that there is a correlation between the two particles' properties in the first place. If particle B's properties seem random when compared to particle A's when measured, then how can we know there is a correlation?

I believe it comes down to knowing that the source of entangled particles is working properly.  You can do this by measuring a lot of the entangled particle pairs coming from it.  If they're entangled, you should start to notice correlations, and at some point you can be statistically confident that you have a source that's generating entangled particles. Once you're confident your particles are entangled, you can exploit that entanglement.

3) How does particle 'splitting' affect entanglement?
If I have two photons A and B that are entangled, and I send A through an extremely powerful magnetic field so that it splits into two weaker photons A1 and A2, will both of these new photons be entangled with photon B? Will only A1 or A2 be entangled with B but not both A1 and A2? Will photon B split as well?

I don't know the answer, but here's my intuition: You have to know what variable you're entangled with respect to, and you have to  treat your particles as a system.  For example, let's say your particles are entangled so that the spin of B is always opposite to the spin of A.  Then let's say that you split A into A1 and A2, both of which have the same spin as A.  Now, if you measure A1 or A2, you still have 100% correlation with B (since A1 or A2 tells you the spin that A had and that tells you the spin B must have).   However, if you split A into A1 and A2 which have opposite spin, then you lose your correlations.  If you measure A1 or A2, you learn nothing about the spin of B.  Losing entanglement through interaction with the environment is called decoherence, and is a major obstacle in designing entanglement systems. 

4) Can two dissimilar particles be entangled?
Can a photon be entangled with an electron? Can a quark in a proton be entangled with a quark in a neutron?

I don't see why not.

[lyner]

I thought entanglement was a result of mutually exclusive quantum numbers. That could only apply to pairs (sets?) of identical particles because it would only be identical particles in a particular system which would have the same set  of quantum numbers.
Anyone put me right on this?

[JP]

I thought entanglement was a result of mutually exclusive quantum numbers. That could only apply to pairs (sets?) of identical particles because it would only be identical particles in a particular system which would have the same set  of quantum numbers.
Anyone put me right on this?

I think what you're describing is the Pauli exclusion principle: that two fermions cannot have completely identical quantum states in a system.  This could give rise to correlations in a helium atom's electrons, for example.  If you measure one electron's spin, you know the other's spin has to be opposite (due to the exclusion principle).  However, in dealing with photons you can't invoke this, since photons are Bosons, and it's possible for identical photons to exist.

[lyner]

OK, that makes sense; photons are bosons. So how can they become quantum entangled? How does the state of one involve the state of another one? What can you do to entangle them? The idea of one electron state being relevant to another electron seems to make sense but, for two photons. . . .?

[lyner]

I have read around a bit and most of the web pages are too hard to get started on BUT this is more approachable:
http://www.davidjarvis.ca/dave/entanglement/index.shtml
There is a lot of elementary stuff which leads to a sensible discussion of QE with practical applications - unlike many of the pages, elsewhere, which assume you know all about it in any case.
I now realise that I've been here before. The  way that photons follow macroscopic wave rules must involve quantum entanglement  and many polarisation effects need quantum entanglement to reconcile particle behaviour with classiclal wave theory.
Some sort of ' exclusion principle' would seems to apply in all cases of QE of any two particles; for instance, electron diffraction / interference; an electron on its way through a double slit will have either one or another set of quantum numbers to describe its  'path' but, until it has actually been observed in a particular place, there are a large number of possible sets of numbers that will satisfy the wave description of the interference pattern.

Perhaps the Pauli Exclusion Principle (in particular) and the distinction between bosons and fermions relates to  particles in a bound state is not relevant for 'free particles'. 

The old chestnut about 'how big is a photon' can involve the idea of quantum entanglement when you have to decide which atom a photon is actually going to be absorbed by.  In fact, QE seems to be everywhere around us.
The clever thing about making actual use of QE seems to be to set up an experiment in which the possible outcomes are limited in some way so that you can demonstrate it at work and to use the entanglement to some useful end or to demonstrate its existence.

[Kryptid (OP)]

Would it be possible to have, say, two iron atoms whose electrons are entangled with one another? By this, I mean that one of the electrons in the 1s orbital in one of the atoms is entangled with its correspondent in the 1s orbital of the other atom, and the same for all of the other electrons as well. If I had a sphere of iron all of whose electrons (or even nuclei) were entangled with all of the correspondenting electrons in another sphere of iron of equal molarity, would manipulation of one of these spheres cause noticeable changes in the other sphere? If I spin one, would the other spin too? What if I moved one of them? Would the other move?

[Soul Surfer]

You are mixing up quantum and classical thinking.  What you describe could not happen.  The moment one particle interacts with another the entanglement is lost and entanglement can only be maintained in isolated atoms.  Atoms in solids are continually interacting with each other because thast's what makes them a solid.  photons are best for this because they do not interact with each other in a vacuum