It's easier to explain with an example. Let's pick the easiest example. [1]
In the easiest example, imagine that you have two boxes, with an entangled particle inside. If you open one box, the entanglement is broken and you can see 50% of the time "yes" and 50% of the times "no". The particles are entangled in a way that if you open the other box, you will see the same result.
The box can be used only once. Once it it open, the result is fixed forever. Also, to produce the box, they must be together. [3]
Now you transport one box to the opposite side of the Earth or the galaxy, or whatever.
If you open one box, you have a 50% chance of seeing "yes" and a 50% chance of seeing "no". That's all. It's just a coin. You can't choose to see "yes" or "no". You don't know if the other box is still closed or is already opened.
The only interesting part is that is that if you ever get in contact with the persons that have the other box, and if they have opened the box (perhaps before you, perhaps after you) you can talk and you will notice that they got the same result.
But when they opened the box, they can't choose to see "yes" or "no". And they don't know if your box is still closed or is already opened.
So you can't encode a secret message, and choose wisely the results of lot of boxes that you have in storage to transmit the secret message like with a radio
But you can use it to generate a random shared number.
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Back to the black hole scenario. Let's imagine that they were traveling to the other side of the galaxy and they made a navigation error and were swallow by a black hole [4]. But you didn't notice.
If you open one box, you have a 50% chance of seeing "yes" and a 50% chance of seeing "no". That's all. It's just a coin. You can't choose to see "yes" or "no". You don't know if the other box is still closed or already opened. You don't know that they entered the black hole. You don't know if they opened the box before entering the black hole. You don't know if they opened the box after entering the black hole. You have a 50% chance of seeing "yes" and a 50% chance of seeing "no". That's all.
They can't transmit information from inside the black hole, but they neither can transmit information using the box from the lab in the other floor of the building.
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Now, if you later realize they went into the black hole, and you try a rescue mission [5]. You will be also swallow by the black hole, and if it is huuuuuuuuuuuge back hole that don't kill you and give enough time, then you can meet them and compare notes, and you will you will notice that they got the same result. [6]
[1] Note that there are more complicated examples, that are very important.
[2] In other examples they may have the opposite result, or something more weird, or more than two options.
[3] Yes, there are more complicated options.
[4] It is sad, but science must go on.
[5] This is really a bad idea.
