What is quantum entanglement?

A simple example

The best-known entangled state of two qubits is a Bell state:

(|00⟩ + |11⟩) / √2

It means "both qubits are 0, or both are 1", in superposition. Measure the first qubit and you get 0 or 1 at random, 50/50. But whatever you get, the second qubit will give the same answer when you measure it, even if it is on the other side of the world.

Crucially, you cannot write this state as "qubit A is in some state, and qubit B is in some state". The information is in the relationship, not in either qubit on its own. That is what entanglement means.

Isn't that just like a pair of gloves?

Put one glove in each of two boxes and post them to different cities. Open one box, find a left glove, and you instantly know the other is a right glove. Nothing spooky happened: the gloves were left and right all along.

For a long time, physicists wondered whether entanglement was just like that, with hidden properties settled in advance. In 1964 John Bell showed that the two ideas make different predictions. If you measure entangled particles in several different directions and compare the results, any "decided in advance" explanation has to obey a limit, now called a Bell inequality. Quantum mechanics predicts that entangled particles break that limit.

Experiments by John Clauser, Alain Aspect, Anton Zeilinger and many others found that they do break it. In 2015, several teams closed the remaining loopholes, and in 2022 Aspect, Clauser and Zeilinger shared the Nobel Prize in Physics for this work. Entanglement is real, and it is not just hidden information.

"Spooky action at a distance"

Albert Einstein was uneasy about entanglement and famously called it "spooky action at a distance". In 1935, with Boris Podolsky and Nathan Rosen, he argued that quantum mechanics must be incomplete.

It is natural to wonder whether entanglement lets you send a message instantly. It does not. Each person on their own sees only random 0s and 1s. The correlation only becomes visible when the two sides compare their results, and that comparison has to travel by ordinary means, no faster than light. This is called the no-signalling principle.

How to make entanglement

In a quantum computer, two gates are enough. Start with two qubits in |00⟩. Apply a Hadamard gate to the first, putting it into an equal superposition, then a CNOT gate, which flips the second qubit only if the first is 1. The result is the Bell state above. You can read more about these in what quantum gates are.

Why quantum computers need it

Without entanglement, a quantum computer would be easy to simulate: you could track each qubit separately with a handful of numbers. Entanglement is what forces the description to grow to 2ⁿ amplitudes for n qubits, which is where the potential advantage comes from. It is a necessary ingredient, though not a sufficient one: some highly entangled circuits can still be simulated efficiently.

Other uses

• Quantum key distribution: entangled pairs can be used to share secret keys in a way that reveals any eavesdropper.
• Quantum teleportation: an unknown qubit state can be transferred using an entangled pair plus two ordinary bits of information. Nothing travels faster than light, and the original state is destroyed in the process.
• Quantum sensing: entangled particles can measure some quantities more precisely than independent ones.
• Quantum networks: linking quantum computers together by sharing entanglement between them.