Two Readouts That Always Agree
Take two qubits, both at |0⟩. Apply a Hadamard gate to the first, which puts it in an equal superposition of 0 and 1. Then apply CNOT, which flips the second qubit wherever the first is 1. The pair is now in the state (|00⟩ + |11⟩)/√2: an amplitude of 0.71 for both reading 0, an amplitude of 0.71 for both reading 1, and nothing for the mixed readouts 01 and 10.
Measure the first qubit and you get 0 or 1 with equal odds. Measure the second on its own and you get the same coin toss. Measure both and the results always match. If the first reads 1, the second reads 1, whether it is measured a nanosecond later or a year later on the far side of the planet. The mixed readouts never happen.
What makes this entanglement rather than a coincidence is that neither qubit has a state of its own. There is no point on the Bloch sphere that describes the first qubit alone; every description of it has to mention the second. The pair has a definite state and the parts do not.
Why It Is Not a Shared Secret
The obvious explanation is that the two qubits agreed on their answers at the source, like a pair of envelopes that each contain the same card. Einstein, Podolsky and Rosen argued in 1935 that something like this had to be true, and that quantum theory was therefore incomplete. The missing agreed answers are called hidden variables.
In 1964 John Bell showed that the envelope picture makes a testable prediction. If each observer can choose between several measurement directions, then any pre-agreed table of answers limits how often the results can agree across the different choices. Quantum theory predicts agreement beyond that limit. In the standard version of the test, any table of pre-agreed answers scores at most 2, and quantum theory predicts about 2.83.
The experiments have gone quantum theory’s way every time. John Clauser ran the first test in 1972, Alain Aspect closed the loophole of slow measurement choices in 1982, and in 2015 groups in Delft, at NIST and in Vienna closed the remaining loopholes at once. Aspect, Clauser and Anton Zeilinger shared the 2022 Nobel Prize in Physics for this work. The result is that the readouts were not decided in advance by any information the qubits carried with them. The randomness described in Superposition, Measurement and Interference is real.
No Message Travels
Entanglement cannot be used to send a signal. Alice’s readouts are a fair coin whatever Bob does, and Bob’s are a fair coin whatever Alice does. Bob cannot tell from his own results whether Alice measured first, measured in a different direction or measured at all. The correlation becomes visible only when the two lists of results are brought together and compared, and that comparison travels by ordinary means, no faster than light.
Einstein’s phrase for the effect was “spooky action at a distance”, and the phrase has outlived his objection. Nothing acts at a distance in a way that could carry a message. What entanglement provides is a shared resource. Quantum teleportation, for instance, moves a qubit’s state from Alice to Bob using one entangled pair plus two ordinary bits sent over a classical channel, and it does not work without the classical bits.
Entanglement Inside a Quantum Computer
A single qubit holds two amplitudes. Two independent qubits hold two each, and you can keep track of them separately. Two entangled qubits hold four amplitudes that cannot be split into two lists of two. Thirty entangled qubits hold about a billion amplitudes with the same property. That is where the exponential size of a quantum computer’s state comes from, and it is also why such states are so hard to simulate classically: there is no shortcut that treats the qubits one at a time.
| Step | 00 | 01 | 10 | 11 | Entangled? |
|---|---|---|---|---|---|
| Start: both qubits at 0 | 1 | 0 | 0 | 0 | No |
| H on the first qubit | 0.71 | 0 | 0.71 | 0 | No: the second qubit is still simply 0 |
| CNOT, first controls second | 0.71 | 0 | 0 | 0.71 | Yes: neither qubit has its own state |
Entangling gates are the hard part of every platform. Single-qubit rotations are routinely performed with errors below 0.01%. Two-qubit gates such as CNOT are ten to a hundred times worse: Quantinuum reports 99.921% fidelity for the two-qubit gates on its Helios trapped-ion machine, and the best superconducting processors report above 99.5%. Those numbers, rather than qubit counts, decide how long a computation can run before errors swamp it. The animated walkthrough shows the H and CNOT sequence as step 6.
Noise is entanglement too. When a qubit interacts with a stray field or a vibrating atom in its substrate, it becomes entangled with its environment, and the environment is never measured. From the computer’s point of view the qubit’s amplitudes have lost their relationship to each other. This is decoherence, and Quantum Hardware and Error Correction explains how machines fight it.
Entanglement and encryption
Shor’s algorithm entangles a register of qubits with the output of a mathematical function, so that interference across the whole register reveals the function’s period. That is the step that breaks RSA and elliptic curves; Shor, Grover and the Quantum Speedup explains it. Entangled photons are also the basis of some quantum key distribution systems. OWL uses neither: its post-quantum encryption is mathematics that runs on ordinary devices.
Sources & Further Reading
- A. Einstein, B. Podolsky and N. Rosen, “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?”, Physical Review 47, 777 (1935).
- J. S. Bell, “On the Einstein Podolsky Rosen paradox”, Physics Physique Fizika 1, 195 (1964).
- B. Hensen et al., “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres”, Nature 526, 682 (2015); NIST, “NIST Team Proves ‘Spooky Action at a Distance’ is Really Real” (2015).
- The Nobel Prize in Physics 2022: press release and popular science background.
- The Quantum Atlas: Quantum Entanglement, Joint Quantum Institute, University of Maryland.
- M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2010), sections 1.3.7 (teleportation) and 2.6 (EPR and the Bell inequality).
- Quantinuum, “Introducing Helios” (November 2025): the two-qubit fidelity figure quoted above is company-reported.