A classical optical switch reads a voltage that is always definitely high or low, so a light pulse is deterministically sent to one port — pick |0⟩ or |1⟩ above and every photon goes the same way, every time.
A quantum-controlled switch instead couples the photon's path to a control qubit. Prepare the qubit in superposition cos(θ/2)|0⟩ + sin(θ/2)|1⟩ and the photon becomes entangled with it — it travels both output arms at once (the translucent "ghost" paths) as a coherent superposition, not as a hidden coin flip decided at the switch. Detecting the photon at one port and reading the qubit's final state always agree — that perfect, run-after-run correlation between a supposedly-random photon outcome and the qubit's collapse is the fingerprint of entanglement, and is what a purely classical random switch cannot reproduce.
- θ = 0° — qubit is |0⟩, photon always to Port A.
- θ = 180° — qubit is |1⟩, photon always to Port B.
- 0° < θ < 180° — genuine superposition; run many trials to see the measured split converge on cos²(θ/2) / sin²(θ/2), while every single trial still shows perfect qubit/port correlation.