How entangled photons turn eavesdropping into something that cannot be hidden
Imagine two magic coins. Each one alone lands completely at random. But if Alice and Bob toss them “at the same angle”, the coins always land on opposite sides — no matter how far apart they are. That is quantum entanglement: each result is random, yet together they are coordinated.
The E91 protocol, proposed by Artur Ekert in 1991, uses this property to obtain keys whose eavesdropping cannot be hidden. Unlike BB84, where Alice prepares the photons herself, in E91 they come from a source of entangled pairs, and eavesdropping is given away by the Bell test.
The measurement results of entangled photons are linked at any distance, although each one alone is random. You cannot send a message this way — the link only shows up when Alice and Bob compare notes.
Alice and Bob measure the photons' polarization by turning a polarizer. Each of them has three angles, and for every pair the angle is chosen at random.
0°, 22.5° and 45°
22.5°, 45° and 67.5°
22.5°/22.5° and 45°/45° — the bits go into the key
The closer Alice's and Bob's angles are, the more often their bits are opposite: at equal angles — always, at a 22.5° difference — 85% of the time, at 45° — a coin flip, at 67.5° — only 15%.
Exactly this dependence on the angle is impossible in the classical world. It is what gets checked to make sure the photons are still entangled.
E91 uses entangled photon pairs distributed between Alice and Bob. Let's walk through the process step by step:
The source creates entangled photon pairs and sends one photon to Alice and the other to Bob. If both measure their photons at the same angle, their bits always turn out opposite.
Alice and Bob independently and at random pick one of their three angles and record the result: 0 — the photon passed the polarizer, 1 — it did not.
At equal angles the bits are always opposite. At different angles, the bigger the difference, the more often the bits match. Each bit alone is random.
Over the public channel, Alice and Bob announce which angles they chose — but not the results.
Pairs with equal angles go into the key: Bob flips his bits and gets a copy of Alice's bits. Pairs with Alice at 0°/45° and Bob at 22.5°/67.5° go to the Bell test. The rest are discarded.
Alice and Bob reveal the test pairs completely. Each round has a goal: at 0°/67.5° the bits should match, in the other combinations they should differ. If the photons had pre-arranged answers (a “cheat sheet”), no cheat sheet could win more than 75% of rounds. Entangled photons win about 85%.
If the win rate is clearly above 75% and the key has few errors, entanglement is intact and Eve knows little about the key: the key is corrected and compressed. If the win rate is 75% or lower, the photons behaved like ordinary ones — someone measured them — and the key is discarded.
In the E91 simulation, you will:
You don't just read about quantum entanglement — you test it yourself. You'll see how the gap between 75% and 85% wins becomes an eavesdropping detector, and understand why E91 is called one of the most beautiful protocols in quantum cryptography.
Bell inequalities are mathematical conditions that must hold in any classical local theory. If you measure entangled particles and violate these inequalities, it means the system is genuinely quantum and entangled.
In E91 the Bell test uses the pairs where Alice's and Bob's angles did not match. Physicists write it with correlations E = (matches − mismatches) / total and the number S = E₁ − E₂ + E₃ + E₄ (the CHSH inequality). The Bell game win rate equals 1/2 + |S|/8: the classical limit |S| ≤ 2 is 75%, the quantum maximum 2√2 ≈ 2.83 is about 85%.
Proof that no local hidden-variable theory can reproduce all the predictions of quantum mechanics
The Einstein-Podolsky-Rosen thought experiment, which tried to show quantum mechanics was "incomplete" but instead led to the discovery of entanglement
The first experimental confirmations of Bell inequality violations in the 1980s, proving the reality of quantum entanglement
For the Bell test each side needs two angles: Alice 0° and 45°, Bob 22.5° and 67.5°. The key needs equal angles — 22.5° and 45°. Three angles each is the smallest set that gives both. Ekert's paper gives the angles 0°, 45°, 90° for spins; for photon polarization they are halved.
How E91 differs from BB84:
The E91 protocol was proposed by Artur Ekert in 1991. It was the first quantum key distribution protocol to explicitly use the violation of Bell inequalities to detect eavesdropping.
Fun fact: Ekert was inspired not just by cryptography but by fundamental questions in quantum mechanics. His protocol became a bridge between "pure" quantum physics and practical applications in information security.
Today, the E91 protocol and its variants are used in:
Now that you understand the magic of quantum entanglement and the E91 protocol, it's the perfect time to create your own entangled key!
In the game you'll warm up with entangled photons, start the source, play the Bell game and see how it gives Eve away