Classical vs. Quantum Correlation

Mission 4: Entanglement. Part of the Quantum Courier Service, a free course from the Oxford University Quantum Information Society.

To understand why Internal Affairs is freaking out, you have to understand the difference between a normal coincidence and a quantum coincidence.

The Boring Treasure Map (Classical): Imagine I slice a treasure map in half, seal them in envelopes, hand one to Alice in Oxford, and blast Bob to Mars with the other. When Bob opens his envelope and finds the right half, he instantly knows Alice has the left half. No magic here; the reality was pre-determined the moment I sealed the envelopes.

The Voodoo Coins (Quantum): Entanglement is completely different. We use our glitched machine to mathematically glue two qubits together into a "Bell Pair". We hand one coin to Alice and ship the other to Bob. Right now, neither coin has a value, and neither is secretly Heads or Tails waiting to be found out. They are both pure, uncollapsed probability.

The Match: Alice slams her hand down, measures her qubit, and gets a "1" (Tails). When Bob measures his own coin, 225 million kilometers away, he gets a "1" (Tails) too. Run it again with a fresh pair and they might both land "0" this time, but the uncanny part never changes: every single time Alice and Bob later compare their results, the two coins agree, provided they both asked the same question. Ask different questions and the agreement softens, which is a thread we pick up in Module 5, and it's the thread the whole protocol hangs from.

Here is where almost every recruit goes wrong. Alice's measurement did not reach across the vacuum and shove Bob's coin into place. Bob, staring at his own coin, sees nothing special at all, just a plain 50/50 result, identical whether or not Alice has measured. The "spooky" pattern only surfaces once the two of them lay their results side by side. They didn't agree to be Tails before Bob left Earth, and no signal raced between them. What they share is not a pre-agreed answer but a single state that has no separate halves. The pair is one object, described together, right up until someone measures. Einstein absolutely hated this, grumpily calling it “spooky action at a distance”. He was right that it is spooky, and right that nothing crosses the gap. Where he was wrong, and it took Bell eighteen years and an experiment to show it, was in assuming the answers must have been packed into the coins all along. In Module 4's final drill you'll rule that possibility out yourself, with your own data.