08 · The system
Decoherence
The world is a measurement you did not schedule. Off-diagonal amplitudes decay. Same Z-probabilities, no interference. The fridge, the pulses, and error correction are the harness.
In English
The fridge, the air, a stray photon — the world is always measuring a little. The arrow shortens in the equator (phase leaks). Chances of 0 and 1 can look the same while interference dies. That is why hardware is hard.
- Try this
- Turn up the decay. Try the interference trick from earlier. It should fail even though the Z-chances barely moved.
- Keep this
- Decoherence is an unscheduled measurement. Error correction is the harness.
Lab · lose the off-diagonals
Start in |+⟩. Z-probabilities stay 50/50 no matter how much phase you leak. Put an H on top — a pure |+⟩ becomes |0⟩ for sure. A fully decohered |+⟩ is just a coin, and H of a coin is still a coin.
Equatorial length 1.00 · z 0.00
Density matrix ρ
[[ 0.5 , 0.5 ] [ 0.5 , 0.5 ]]
- P(|0⟩) before H
- 50.0%
- P(|0⟩) after H
- 100.0%
Almost pure. H maps |+⟩ to |0⟩.
The harness around a qubit
The vector
State
A pure qubit is a direction. Decoherence does not rotate it. It shortens the projection onto the equator — the part that can still interfere.
A density matrix ρ is how you write a state when you might have lost the phase. For a pure state, ρ = |ψ⟩⟨ψ|. Decoherence damps the off-diagonal entries. Populations (the diagonal) can sit still while interference dies.
That is why a qubit is hard, and why Volume I’s “harness” has a twin here: isolation, control, and error correction around a fragile engine.