entanglement

Imagine you and a friend each get a sealed envelope and walk to opposite ends of the Earth. When you open yours, you instantly know something about what is in your friend's. Entanglement is a far stranger version of this: two or more qubits end up in a single shared state that you cannot fully describe by talking about each qubit on its own. The whole is real; the parts, taken separately, are not the full story. Measure one qubit, and the outcome statistics of its partners are immediately constrained, even if they are far apart.

More precisely, an entangled state is one that cannot be written as a separate state for each qubit multiplied together; the joint state is non-separable. The classic example is a Bell pair, where two qubits are perfectly correlated: if you measure one as 0 the other will read 0 too, and if one is 1 so is the other, yet before measurement neither qubit has a definite value of its own. This shared correlation is a genuine resource, and it is what powers protocols like quantum teleportation and helps drive the speedups in many quantum algorithms.

It is worth being honest about what entanglement is not. It does not let you send messages faster than light: the local outcomes you see look completely random, and only when you compare notes over an ordinary (slower-than-light) channel do the correlations become visible. Entanglement is also fragile, leaking away through noise and decoherence, which is one of the central engineering challenges of building real quantum computers today.