The particles in that video are both red and blue -- a visual representation of not really their color, but their particle spin state. The particle has both properties at any given time.
In quantum physics, it is a game of probability that we deal with. Does the light travel straight, curve left, or curve right? Quantum physics say it does all 3, but the probability that it will travel straight is the greatest. However, when you block the straight path, you find that it still gets to the point behind the wall, because it curved left or curved right to get around the wall. You can find details on this experiment if you want to follow up on it.
In any event, it is only when you take and measure whether it is spinning left or right, let's say we take a picture of it and then look to see if it is red or blue, that you see one state captured in that moment. When we take a picture of both particles, whenever one is shown to be red, the other is always guaranteed to be blue. You never find both red or blue at the same time.
It is as if they are one, where the spin is alternating between them.
What the video did not show is that if you then bring in a 3rd particle in, and let's say this one can either be red or purple (spin left, spin up) and you entangle it with particle one, then when you take a picture of all 3, you get the following results:
1. P1 is red, P3 is purple, and some distance away P2 is blue.
2. P1 is blue, P3 is purple, and some distance away P2 is red.
3. P1 is blue, P3 is red, and some distance away P2 is purple.
2. P1 is red, P3 is red, and some distance away P2 is purple.
Wait, how can P2 be purple? It was only ever red or blue to start with.
This is the power of entanglement. You can transmit new information over great distances via entangled matter.
For more details, please check the link: