Quantum Mechanics demystified, a try
It’s like a pair of gloves. You normally have them both, right and left.
But you could send one for Liisa, say the left hand one, and the other for Pekka. Once Liisa receives her glove, she knows right away that Pekka is receiving the right hand one.
No mystery in that.
The same can go on with particles, e.g. between electrons in Cooper pair.
In Cooper pair two electrons get bound together in low temperature superconducting state. These bound electrons must have opposite spins. They can be separated by a device called SET - Single-electron transistor. Once these electrons are transferred apart from each other, in leads of the SET, the spins are remaining opposite to each other.
No mystery in this either. It’s only hard to keep track where ever entangled electrons lie with limited human perception.
Which makes the whole stuff hard to catch for us humans.
A remarkable feature of entangled systems is related to vector factorization. A vector is factorizable (or separable) if it can be written as a tensor product of two other vectors. Otherwise is is unfactorizable. A compound quantum system can be presented as a vector.
E.g. the state of two electron system can be presented by some vector v. If this vector v is not factorizable, these two electrons are entangled. Meaning that if we measure the state of one of the electrons, we immediately know the state of the other.
On the other hand, if we have such a entangled state vector for a system of two electrons and get hold on one of the electrons, we know that the entangled counterpart must exist somewhere. Non-locally perhaps. As in the ‘Cooper pair SET’ example above.