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Whenever they interact.

Consider the standard example. Two electrons are created in an interaction that has zero net rotation. Each individual electron has some intrinsic rotation (known as spin). So, we know that their spins have to be in opposite directions.

This is analogous to the classical case. If a stationary ball explodes into two fragments, we know those fragments must be rotating in opposite directions, because the initial object had zero net rotation. The interaction (pushing off each other during the explosion) establishes the relationship, and the overall state of the system before the interaction determines the exact values each final object can have.

So far, this doesn’t really sound that quantum. The weirdness of entanglement comes in because of superposition – the fact that quantum particles exist in multiple states (locations, energy levels, or indeed directions of rotation), and will randomly collapse into a single one of these values when you actually measure it. Those electrons aren’t just spinning along a single direction, they each have some probability to be spinning in one of several directions. And most importantly, whenever one of them collapses into a particular spin state, the other one immediately knows about it.

For example each electron could have a 50% chance of spinning either clockwise or anticlockwise. When you look at one, it will randomly collapse, and you will observe either one or the other orientation. If someone then looks at the other electron a minute later, their observation will always be opposite to yours, whether the electron was a meter away or a light year away. Somehow these electrons remain undetermined, but related, no matter how far apart they are.

That’s really what separates quantum entanglement from classical ‘entanglement’, which we don’t even have a special name for – it’s just the fact that when things interact, they affect each other in a quantifiable way.

Edit: Removed some technical terms and defined superposition in more detail.