Quantum cryptography
Protocols such as E91 (Ekert, 1991) build secret keys from entangled pairs. An eavesdropper disturbs the correlations and shows up in the Bell statistics.
01 · The idea
What is entanglement?
In quantum mechanics, a particle's properties such as spin or polarisation are described by a state that can hold several possibilities at once. When two particles interact in the right way, they can end up sharing a single state. From then on you cannot describe either particle on its own. Only the pair has a description.
Take the singlet state above. Each electron, measured alone, shows spin up or down at random, 50/50. Yet if you measure both along the same direction, the results are always opposite. Measure along different directions, and the agreement changes smoothly with the angle between them, following a cosine curve.
That cosine curve is the fingerprint. No theory in which each particle secretly carries pre-set answers can reproduce it. This was proved by John Bell in 1964 and confirmed in the lab many times since.
Why quantum is stranger
Entangled particles let you choose which question to ask: any angle you like. Pre-set answers cannot match the quantum statistics for every possible pair of angles at once. The gloves had no left or right until someone looked.
But no messages travel
Each side alone sees pure randomness. The correlation only appears when the two lists of results are compared, which needs an ordinary, light-speed channel. Entanglement cannot send a signal faster than light.
02 · Interactive lab
Measure entangled pairs yourself
A source creates electron pairs in the singlet state and sends one to Alice (green) and one to Bob (pink). Set each detector's angle, then measure. Your results are plotted against the quantum prediction and the best any “pre-set answers” model can do.
Source and detectors
Same angle → always opposite. Try 0° and 180° for always equal.
Pairs at this angle0
Results opposite–
Quantum predicts–
Correlation vs angle difference
Correlation E = (agree − disagree) / total
Quantum: −cos θ
Best pre-set answers model
Your measurements
Run a Bell test (CHSH)
Four angle settings, 4,000 pairs. Any pre-set answers model gives |S| ≤ 2. Quantum mechanics allows up to 2√2 ≈ 2.83.
02 · classical limit2.83
Press the button to collect data.
03 · Timeline
From paradox to Nobel Prize
- 1935
The EPR paradox
Einstein, Podolsky and Rosen argue that quantum mechanics must be incomplete: if measuring one particle fixes the other's result, the values must have existed in advance.
- 1935
Schrödinger names it
Erwin Schrödinger coins the word “entanglement” (Verschränkung) and calls it the characteristic trait of quantum mechanics.
- 1964
Bell's theorem
John Stewart Bell shows the question can be tested. Local hidden-variable theories obey an inequality that quantum mechanics violates.
- 1972
First Bell test
Stuart Freedman and John Clauser measure entangled photons from calcium atoms. The results side with quantum mechanics.
- 1982
Switching detectors in flight
Alain Aspect's team in Paris changes measurement settings while the photons travel, closing a key loophole.
- 1997
Quantum teleportation
Anton Zeilinger's group in Innsbruck teleports the quantum state of a photon using entanglement plus a classical message.
- 2015
Loophole-free tests
Teams in Delft, Vienna and at NIST close the main loopholes at the same time. Local realism is ruled out.
- 2017
Entanglement from space
China's Micius satellite distributes entangled photons to ground stations about 1,200 km apart.
- 2022
Nobel Prize in Physics
Aspect, Clauser and Zeilinger share the prize “for experiments with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science.”
04 · Applications
What entanglement is good for
Quantum teleportation
Moves a quantum state from one place to another using a shared entangled pair and two classical bits. Matter does not travel, and nothing goes faster than light.
Quantum computers
Entangling gates link qubits so a computer can work with correlations no classical machine can store efficiently. Without entanglement there is no quantum speed-up.
Quantum sensing
Entangled atoms and photons can beat the standard noise limit, sharpening atomic clocks, interferometers and gravitational-wave detectors.
05 · Clearing things up
Myths and facts
MythEntanglement lets you send messages faster than light.
FactThe no-communication theorem forbids it. Each side's results look random until compared over a normal channel.
MythThe particles were just like the gloves: the answers were fixed from the start.
FactBell tests rule out every local pre-set-answer model. The lab above shows the gap: |S| above 2.
MythOnce entangled, always entangled.
FactEntanglement is fragile. Stray interactions with the environment (decoherence) destroy it, which is why quantum hardware is kept so cold and isolated.
MythIt only works for tiny distances.
FactEntanglement has been shared over more than 1,000 km via satellite, and the correlations do not weaken with distance.
06 · Key terms
A short glossary
- Superposition
- A quantum system holding a combination of possible states until it is measured.
- Qubit
- The quantum version of a bit, which can be 0, 1, or a superposition of both.
- Singlet state
- The two-particle state |Ψ⁻⟩ with total spin zero. Measured along the same axis, the two spins always come out opposite.
- Bell inequality
- A limit on correlations that every local hidden-variable theory must respect. The CHSH form says |S| ≤ 2.
- Tsirelson's bound
- The largest value quantum mechanics allows for S: 2√2 ≈ 2.83.
- Decoherence
- Loss of quantum behaviour as a system becomes entangled with its noisy surroundings.