Anton Alyakin
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The machine and its matrix
A prepared state and knob axis on a Bloch sphere, two lamps with editable labels and probabilities, and the Hermitian matrix those settings define.
Qubit machine with matrix
Bloch sphere with state and knob axis, two lamps with probabilities, and the corresponding two by two Hermitian matrix.
+1
−1
lamp A
+1
100%
lamp B
−1
0%
A =
1.00
0.00
0.00
−1.00
⟨A⟩ expected
1.00
state tilt
0°
state swing
0°
knob tilt
0°
knob swing
0°
lamp labels
σz
σx
σy
|0⟩⟨0|
identity
run once
run ×100
reset tally
runs 0
σz, then σx, then σy.
Same labels, knob rotated. The ones jump off-diagonal, then go imaginary.
Identity, then spin the knob.
All four entries stay frozen. Both lamps read the same number, so direction means nothing.
Trace and determinant.
The sum and the product of your two labels. Turn the knob and they hold; retype a label and they move.
The check that matters.
The observed mean converges on ⟨A⟩, which is just ⟨ψ|A|ψ⟩. Experiment on the left, arithmetic on the right.
← all three instruments