What Is Quantum Entanglement? Correlations That Cannot Be Explained Locally

Two or more particles are entangled when the quantum state describing them cannot be written as a combination of separate states for each one: the system has a joint description and the individual particles do not have definite properties of their own. A standard example is a pair produced with total spin zero, so that whichever direction you measure, the two results must be opposite. Before measurement, neither particle has a definite spin along any axis, and the theory says this is not ignorance but the actual state of affairs. When one is measured, the joint state resolves and the other particle's result is fixed, whatever the separation. The essential point, and the one lost in most popular accounts, is that no information travels: the result of each individual measurement is random, and the correlation only becomes visible when the two sets of results are brought together and compared, which requires ordinary communication at or below the speed of light.

In 1935 Einstein, Boris Podolsky and Nathan Rosen published a paper arguing that quantum mechanics must be incomplete. Their reasoning was that if measuring one particle lets you predict the other's property with certainty without disturbing it, that property must have been real all along, and since the theory does not include it, the theory is missing something. The proposed missing ingredient is called a hidden variable: some property carried by each particle from the moment of creation, determining what each measurement will find, with the apparent randomness being our ignorance of it. This is a perfectly sensible position and it preserves locality, meaning that nothing influences anything else faster than light. For nearly thirty years the argument was regarded as philosophy, because nobody saw how to test it.

In 1964 John Bell showed that the question was experimentally decidable, which is one of the most consequential results in twentieth-century physics. His argument runs as follows:

• •Assume each particle carries hidden variables determining the outcome of any measurement, and that a measurement on one cannot influence the other, which is the local realist assumption
• •Consider measuring the two particles along various relative angles and counting how often the results agree
• •Under any such theory, the correlations must satisfy a mathematical inequality, which sets a ceiling on how strongly the results can be correlated across different angle choices
• •Quantum mechanics predicts correlations that exceed that ceiling for certain angles
• •So the two are not merely different interpretations of the same predictions: they disagree about numbers that can be measured

John Clauser and Stuart Freedman performed the first test in 1972 and found a violation of the inequality, favouring quantum mechanics. Alain Aspect's group in Paris improved it decisively in 1982 by switching the measurement settings while the particles were in flight, so that no signal travelling at light speed could carry the setting from one detector to the other in time. That left two loopholes, which occupied experimentalists for thirty years: the detection loophole, in which low detector efficiency means the observed sample might not represent all pairs, and the locality loophole, requiring rigorous spacelike separation. Both were closed in the same experiment for the first time in 2015 by groups in Delft, Vienna and Boulder. A further experiment in 2018 used light from distant quasars to choose the measurement settings, so that any conspiracy determining the settings in advance would have had to be set up hundreds of years ago. Clauser, Aspect and Anton Zeilinger shared the Nobel Prize in 2022.

Entanglement is now a resource rather than a curiosity. Quantum key distribution uses entangled pairs to generate a shared secret key between two parties, with the security guaranteed by physics rather than by computational difficulty, since any eavesdropper measuring the particles disturbs the correlations and is detected; systems are commercially available and a Chinese satellite distributed entangled photons between ground stations more than a thousand kilometres apart in 2017. Quantum teleportation transfers the state of one particle to another using an entangled pair and a classical message, which does not move matter and does require the classical channel, so it cannot beat light speed. Quantum computing depends on entanglement for its advantage, since a register of entangled qubits holds correlations that no separate description can capture. And entanglement-enhanced sensing improves the precision of measurements including those in gravitational wave detectors. What it cannot do, despite persistent claims, is send a message, because the individual outcomes are random and only the comparison reveals anything.

Entangled particles share a joint quantum state in which neither has definite properties of its own, so measuring one fixes what the other will show, with correlations stronger than any theory in which each carried the answer from the start. Einstein argued in 1935 that this proved the theory incomplete, Bell showed in 1964 that local hidden variables imply a measurable inequality that quantum mechanics violates, and experiments from 1972 to 2015 confirmed the violation and closed the loopholes. The effect cannot transmit information and underpins quantum cryptography, teleportation and computing.