Two or more qubits sharing a single joint state, so that their measurement results are correlated in ways no classical shared-secret arrangement can reproduce — even though neither qubit has a definite state of its own.
Why it matters
Entanglement is what makes an n-qubit state need 2^n numbers to describe. It powers teleportation, quantum key distribution, and error correction — and it is also the thing pop-science gets most wrong (no, it does not send signals faster than light).
After this you will be able to
Two entangled qubits give perfectly correlated results no matter how far apart they are. But each individual result is random, and you cannot choose what you get. Only by comparing notes over an ordinary channel do the correlations become visible.
Two sealed envelopes that always contain matching cards. Opening yours tells you what the other holds — but you cannot decide which card appears, so you cannot use it to send anything.
Entanglement enables faster-than-light communication.
The no-signalling theorem forbids it. Teleportation, despite the name, still requires two ordinary classical bits to be sent at or below the speed of light.
Where the envelope analogy breaks: for entangled qubits the correlations are stronger than any pre-arranged pair of envelopes could produce. That excess is exactly what Bell inequality experiments measure.
Hand-picked and ordered. If you only have time for one, take the first.
The single best starting point in existence. An essay built on spaced-repetition flashcards embedded in the text, so you actually remember it a month later. Assumes nothing but curiosity, and gets you honestly to quantum teleportation.
Drag gates onto wires and watch amplitudes, Bloch spheres and probabilities update live. Nothing else builds gate intuition this fast, and it needs no install or account.
A rigorous but genuinely well-taught course by John Watrous covering single systems, multiple systems, quantum circuits and the core protocols. The cleanest bridge from intuition to real notation.
Microsoft's concept documentation is unusually well written for docs — the pages on qubits, entanglement and the Q# language work as standalone explanations.
The prize to Aspect, Clauser and Zeilinger for experimentally proving Bell inequality violations. The popular and scientific background documents are excellent free explanations of nonlocality.
Topics that list Entanglement as a prerequisite.