Same Ion Carries State and Motion - Ion-Trap Qubits: Sidebands, Shared Modes, and Fluorescence Readout Step by Step

The same trapped ion carries an internal bright/dark state and a motional packet index, so the source ledger must keep both labels together. The bookkeeping is exact only for the stated bit value, packet index, and ideal shared trap source; laboratory runs add preparation error, state-detection threshold uncertainty, motional heating, mode mixing, and timing or laser-calibration drift.

The ion's internal bit and packet index share one source. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The same ledger carries internal state and motion

The readout state is bright, pinned as bit 1, on the same checked trap source.

b_{\text{readout}}=1

The motion packet remains part of that source

The same source also carries packet index 2 and motional energy 4 joules.

n=2,\quad E_n=4\ \text{J}