What is quantum entanglement?

Einstein disliked the idea and famously called it "spooky action at a distance". Experiments have since shown entanglement is real, and the physicists who proved it, Alain Aspect, John Clauser and Anton Zeilinger, shared the 2022 Nobel Prize in Physics. Today it is a working tool in quantum computing and secure communication.

How does quantum entanglement work?

In quantum physics, a particle such as a photon or electron can be in a superposition: a combination of possible states at once, with only probabilities for what a measurement will show. When two particles interact in the right way, their states can become linked into one shared superposition. Neither particle then has a definite state of its own. Only the pair does.

The simplest example uses two qubits, the basic units of a quantum computer, each of which can be measured as 0 or 1. A common entangled state, called a Bell state, is written:

It means: the pair is in a combination of "both 0" and "both 1". Each has an amplitude of 1/√2, and squaring that gives a probability of ½. Measure the first qubit and you get 0 or 1 completely at random. But the moment you do, the second is fixed: it will give the same result, every time, wherever it is.

Isn't that just like a pair of gloves?

Put one glove of a pair in each of two boxes and send them apart. Open one, find a left glove, and you instantly know the other is right. No mystery: the gloves were left and right all along. Einstein, Podolsky and Rosen argued in a 1935 paper that entangled particles must be like this, carrying hidden instructions from the start.

In 1964, John Bell showed this could be tested. If particles carry hidden instructions, the correlations between measurements made at different angles can only be so strong. Quantum mechanics predicts stronger correlations than any hidden instructions could produce. Experiments since the 1970s have found the quantum predictions every time, so entangled particles are not like gloves: their results aren't settled until they are measured.

Is quantum entanglement real?

Yes. It has been tested thoroughly:

• 1970s and 1980s: John Clauser and then Alain Aspect measured entangled photons and found the correlations broke Bell's limit, as quantum mechanics predicts.
• 2015: a team in Delft ran a loophole-free Bell test with electrons 1.3 km apart, closing the gaps sceptics had pointed to in earlier experiments. Teams in Vienna and at NIST in the US did the same with photons.
• 2017: China's Micius satellite sent entangled photons to ground stations more than 1,200 km apart, and they stayed entangled.

Can quantum entanglement be measured?

Not from a single pair, because one measurement of each particle just gives two random-looking results. Entanglement shows up in the statistics of many pairs. Physicists create thousands of identical pairs, measure each partner at one of several chosen angles, and compare. One standard test, the CHSH version of Bell's test, combines the correlations into a single number, S. Any explanation with hidden instructions gives S of at most 2. Quantum entanglement can reach 2√2, about 2.83. Measuring S above 2 proves the particles were entangled.

Try predicting the results of measuring an entangled pair, then press Mark to check it in our Quantum Computing course.

How fast is quantum entanglement?

The correlation appears to be instant. In a 2008 experiment with photons sent to villages 18 km apart in Switzerland, physicists showed that if some hidden signal passed between the photons, it would have to travel at least 10,000 times faster than light. Most physicists don't think any signal passes at all: the two particles are one system, so there is nothing to send.

Can quantum entanglement be used for communication?

Not to send messages faster than light. Each person sees only random 0s and 1s, and they can't choose which result they get. Only when the two compare notes, over an ordinary channel limited by the speed of light, does the pattern appear. This is the no-communication theorem, and it is why entanglement doesn't break Einstein's rule that nothing travels faster than light.

Entanglement is still very useful for communication in other ways:

• Quantum key distribution: two people share entangled pairs and use the random matching results as a secret key for encryption. An eavesdropper who measures the particles disturbs the correlations, which reveals them.
• Quantum teleportation: the quantum state of one particle can be transferred to a distant particle using an entangled pair plus an ordinary message. The particle itself doesn't move, and the ordinary message keeps it below light speed.
• Quantum networks: researchers are building networks that share entanglement between distant quantum computers.

Entanglement in quantum computing

Entanglement is one of the resources that gives quantum computers their power. A quantum computer creates it with a two-qubit gate called CNOT: put the first qubit into a superposition, apply CNOT, and the pair ends up in the Bell state above. With many entangled qubits, the computer works with a state that would need an enormous amount of memory to describe on an ordinary computer. Algorithms such as Shor's and Grover's rely on entanglement and interference together.

Entanglement is fragile, though. Any stray interaction with the surroundings, from heat or vibration, can break it, a process called decoherence. That is a big reason quantum computers are kept extremely cold and isolated, and why error correction matters so much.

Worked example: are the results really random?

Alice and Bob share 10 pairs in the Bell state above. Each measures their own qubit. What is the chance that Alice's ten results are all 0? Each result is 0 with probability ½, independently from pair to pair, so the chance is (½)¹⁰ = 1 in 1,024. And what is the chance that Bob's results differ from Alice's on any pair? Zero: in this state, they always match. So the results are random one by one, but perfectly correlated pair by pair.

Common mistakes

• Saying entanglement sends signals faster than light. The correlation is instant, but no usable information travels.
• Thinking entangled particles always give opposite results. Some entangled states give matching results, others opposite. It depends on the state.
• Thinking it's like the gloves. Bell tests rule out hidden instructions set in advance.
• Thinking you can check entanglement from one pair. It shows up only in the statistics of many measurements.
• Thinking entanglement lasts forever. Interactions with the surroundings destroy it quickly unless the particles are well isolated.

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