Several single-photon channels, each on its own carrier wavelength λk, were combined onto one shared fiber at the transmitter (multiplexing). At the receiver, this demultiplexer's grating disperses each incoming photon by wavelength and routes it to the output port whose center wavelength is nearest the grating's noisy wavelength read-out.
- Grating measurement noise has fixed width σ (device resolution).
- Channel centers sit Δλ apart, set by how well the transmitter separated them.
- When Δλ ≫ σ the nearest-port decision is almost always correct.
- When Δλ approaches σ, the noisy read-out crosses into a neighbor's decision region — the photon is misrouted to the wrong output port (cross-talk), without its quantum state itself being disturbed.