Drive and Readout Cross-Scans

Fluorescence Threshold Boundary Cross-Scan

Fluorescence readout turns photon counts into a bright-or-dark decision by comparing each count with a threshold. Here 4 photons is dark below the threshold 10, while 10 and 12 photons are bright because the rule accepts counts greater than or equal to the threshold. Real readout also has background light, collection efficiency, state-preparation errors, finite shots, and threshold uncertainty.

Fluorescence readout is a count-threshold rule with a checked equality boundary. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Dark below threshold

The source state bit is 0. Photon count 4 is compared with threshold 10.

4<10⇒bresult=04<10\Rightarrow b_{\text{result}}=0
Dark below thresholdFluorescence count, threshold, and result are checked.photonCount=4 countthreshold=10 countresultBit=0 bit

Bright at threshold

The source state bit is 1. Photon count 10 is compared with threshold 10.

10≥10⇒bresult=110\ge10\Rightarrow b_{\text{result}}=1
Bright at thresholdFluorescence count, threshold, and result are checked.photonCount=10 countthreshold=10 countresultBit=1 bit

Bright above threshold

The source state bit is 1. Photon count 12 is compared with threshold 10.

12≥10⇒bresult=112\ge10\Rightarrow b_{\text{result}}=1
Bright above thresholdFluorescence count, threshold, and result are checked.photonCount=12 countthreshold=10 countresultBit=1 bit

The equality row is bright because the rule is above-or-equal

Counts four, ten, and twelve show the threshold boundary. Ten is accepted as bright because the checked rule is greater than or equal.

rowcountthresholdbresultdark below threshold4100bright at threshold10101bright above threshold12101\begin{array}{c|c|c|c}\text{row}&\text{count}&\text{threshold}&b_{\text{result}}\\\text{dark below threshold}&4&10&0\\\text{bright at threshold}&10&10&1\\\text{bright above threshold}&12&10&1\\\end{array}
Fluorescence threshold cross-scanThe middle equality row is the displayed source.photonCount=10 countthreshold=10 countresultBit=1 bit