The Polarizer Bench

Mission 2: The Art of Quantum Messages. Part of the Quantum Courier Service, a free course from the Oxford University Quantum Information Society.

Enough cocktail parties, recruit. Time for the actual optics bench.

Two dials of chips sit in front of you: the Filter angle and the Photon angle. Pick a value for each, then fire a batch and watch Malus's Law do its thing. That cos²(α−θ) isn't just a formula Dr. Woodward likes writing on the whiteboard, it's the literal fraction of photons that survive a filter tilted at an angle to the photon's own polarization. Only the GAP between the two angles matters: line them up and nearly everything gets through; cross them by 90 degrees and the beam dies completely.

Play with it. Set the photon to 0 and walk the filter round, 30, 45, 60, 90, and watch the green survival bar chase the white theory tick every single time. This is the whole secret of quantum measurement in one graph: the "question" you ask a photon (the filter angle) sets the odds of the answer, and a filter crossed at 90 degrees is a question the photon can never answer yes. That is exactly why Eve, forced to guess the basis blind, can never quietly copy a state without leaving the survival rate wrong.

(A wrinkle for the keen: on the Bloch sphere this same law reads cos²(Δ/2), because a polariser rotated by 45° in the lab is a full 90° away on the sphere. Same physics, two maps.)