A shared red packet source scan checks that each red sideband pulse lowers the shared motional mode by exactly one packet while the addressed ion stays fixed. The three rows move the shared packet from 1 to 0, 2 to 1, and 3 to 2, all with accepted bit 1 exactly for the stated toy sideband ledger; real ion traps depend on laser calibration, motional heating, pulse-area error, state-preparation fidelity, and finite-shot uncertainty.
Accepted red sidebands lower the shared packet source by one. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Accepted red sideband lowers the shared packet by one
The addressed ion stays A. The shared-mode ledger cites the red sideband start and end packets.
nshared:1→0,a=1
Accepted red sideband lowers the shared packet by one
The addressed ion stays A. The shared-mode ledger cites the red sideband start and end packets.
nshared:2→1,a=1
Accepted red sideband lowers the shared packet by one
The addressed ion stays A. The shared-mode ledger cites the red sideband start and end packets.
nshared:3→2,a=1
The shared ledger moves one packet down from each source packet
Each starting packet drops by one shared-mode step. The accepted bit stays high because none of the rows crosses below the boundary.