Entanglement, Carefully

Entanglement attracts more mystical prose than any other idea in physics. The computational content is more modest and more useful.

What it is

Two qubits are entangled when the pair has a definite joint state while neither qubit has a definite state of its own.

Concretely, you can prepare two qubits so that measuring them always gives matching results. Both 0, or both 1, each with 50 percent probability. Neither qubit individually is 0 or 1 beforehand, yet the pair is guaranteed to agree.

Separate them by any distance. Measure one and get 0, and the other will give 0. Measure one and get 1, and the other gives 1. Every time.

Why this is not a secret message

The immediate reaction is that this transmits information instantly. It does not, and the reason is precise.

The outcome you get when you measure your qubit is random. You cannot choose it. You cannot make your qubit come out 1 in order to signal something.

So the distant party sees a random result, exactly as they would if the qubits were not entangled. Only by comparing notes afterwards, over an ordinary communication channel limited by the speed of light, does the correlation become visible.

Entanglement guarantees the results will agree. It does not let you choose what they agree on, and choosing is what sending a message requires.

This is worth being firm about, because faster than light communication is regularly attributed to entanglement in popular coverage and occasionally in marketing. It is not a matter of current engineering limits. It is prohibited.

Then why does it matter?

Because ordinary correlation cannot reproduce the statistics.

You might suppose the qubits simply agreed on an answer in advance, like two sealed envelopes containing the same letter. That explanation works for the simple case above.

It fails for more elaborate experiments. If you measure the two qubits along different, independently chosen directions, the pattern of agreement is stronger than any pre-arranged agreement can produce. This has a precise formulation in Bell's theorem, and the experiments have been performed many times with increasing rigour, closing one loophole after another. The 2022 Nobel Prize in Physics went to this line of work.

The result: the correlations are real and cannot be explained by the qubits having carried matching instructions from the start.

The computational role

For our purposes the role is more concrete.

Entanglement is what makes a quantum computer more than a collection of independent qubits. If your qubits were never entangled, the state of the machine would be describable by listing each qubit separately, which takes an amount of information proportional to the number of qubits. Such a system can be simulated classically without difficulty.

It is entanglement that forces the full 2 to the n description. The whole becomes genuinely more than the parts, and the exponential resource that makes quantum computing interesting appears exactly when qubits become entangled.

Concretely, entanglement lets an operation on one qubit affect the amplitudes of outcomes involving all the others, which is how interference patterns are built across the entire space of possibilities rather than one qubit at a time.

So the three ideas take their places. Superposition provides the possibilities. Entanglement links them so the machine is more than the sum of its qubits. Interference selects the answer.