Schrodinger equation. This equation tells us that the wave function of two particles is an independent function, which describes two particles. If these two particles never interact, it is possible to decompose this equation into two independent equations, one for each particle. But in general, the two-particle equation cannot be factorized. We call this situation entanglement.
If explained by Copenhagen of quantum mechanics, the measurement collapse wave function of any entangled particle will affect the measurement result of another particle. Einstein said that this shows that quantum mechanics is "incomplete", because as far as its present situation is concerned, the theory seems to violate the special theory of relativity. (It should be noted that this was only a purely theoretical discussion at that time, because the role of entanglement has not been observed. )
One year after Einstein's death, Everett pointed out that the collapse hypothesis caused this problem. He suggested giving up the idea of collapse and showed that the expected experimental results were not affected by the existence of collapse. Without collapse, we still have strange entanglement effects, but we don't need any connection faster than light to explain them. On the contrary, we have a multi-world explanation of quantum mechanics, which has multiple copies of observers. The relationship between entangled States can be explained as follows: in the same "world", the observation results of observers are always consistent.
Entanglement has no equation. Because the superposition principle is applied to multi-particle systems, we have entangled quantum States.
This is also an allowable quantum state. However, two possible measurements are missing. This is a state of entanglement.
The key difference between entangled state and non-entangled state is a simplified set of possible measurement results. This means that the measurement result of one particle must be related to the measurement result of another particle. Mathematically, entangled states cannot be decomposed into tensor products of two independent particles, which is how we begin to deal with two-particle systems.
Entangled state is a completely allowable quantum state, but it is called entangled state because it cannot be separated into the product of two independent particle states.
We can understand the properties of some entangled States by comparing non-entangled States with entangled States. Each state consists of a set of possible measurement results. If you measure the state of A as H and you measure the state of B as H, this is not enough information to determine whether the states are entangled, because both possible states may give results. Including entangled and non-entangled states). Therefore, only one state measurement is not enough to determine whether there is entanglement. In fact, you need to do a lot of measurements to build enough statistics to confidently declare that you are observing an entangled state. However, this is still not enough. In fact, you have to make a series of so-called Bell State measurements to prove the violation of Bell Inequality, and use the statistical data generated by many measurements.