Snaring the Quantum Eavesdropper

How eavesdropping breaks quantum correlations

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

Right, look sharp, recruit. This is the drill the whole module has been walking towards, and it is not a spotting game. It is a measurement.

Alice and Bob each hold half of a stream of entangled pairs. Each of them picks, at random, one of two settings to measure in, and writes down the answer. Afterwards they line the two columns up and compute a single number from how often they agreed across the four combinations of settings. That number is called S.

Here is why it matters. If the answers were sitting in the particles all along, packed in at the source, revealed by measurement, with no influence crossing the gap, then S cannot exceed 2. Not "usually doesn't". Cannot. That is a theorem, and it holds whatever the particles are made of and whatever the hidden bookkeeping looks like.

So run it. Let the pairs accumulate and watch S climb past 2 and settle near 2.83. Then flip on classical hidden variable and watch the same apparatus, fed by the best pre-agreed strategy any two separated parties can possibly use, press up against 2 and stop dead. Not because the model is feeble, but because it is at its ceiling.

Give it enough pairs that the error bar shrinks and the gap stops being arguable. That is the snare, and Eve is not what it caught. Chop chop!