Detuning, Readout, and Audit

Far Detuned Mode Is Rejected

A detuning window test rejects a candidate mode when its frequency square lies farther from the target than the allowed tolerance. The candidate with L=1/5 H and C=1 F gives omega squared 5, a distance 4 from target 1 and greater than tolerance 1, so the accepted bit is 0 exactly for the stated ideal LC model; real devices have calibration drift, linewidth, noise, fabrication spread, loss, thermal photons, crosstalk, and readout uncertainty.

A rejected detuning candidate still cites a checked LC 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 far candidate is still a checked LC source

The rejected candidate uses inductance 1/5 henry and capacitance 1 farad, giving square 5.

L=15 H,C=1 F,ω2=5 s−2L=\tfrac{1}{5}\ \text{H},\quad C=1\ \text{F},\quad \omega^{2}=5\ \text{s}^{-2}
Far checked candidateRejected does not mean unchecked.inductance=1 Hcapacitance=1 FlcProduct=1 s^2omegaSquared=1 1/s^2inductance=1/5 Hcapacitance=1 FlcProduct=1/5 s^2omegaSquared=5 1/s^2targetOmegaSquared=1 1/s^2candidateOmegaSquared=5 1/s^2tolerance=1 1/s^2distance=4 1/s^2acceptedBit=0 bit

Outside the tolerance gives accepted bit zero

The distance is 4, greater than tolerance 1, so the accepted bit is 0.

4>1⇒accepted=04>1\Rightarrow accepted=0
Rejected detuningThe rejection is an exact window decision.inductance=1 Hcapacitance=1 FlcProduct=1 s^2omegaSquared=1 1/s^2inductance=1/5 Hcapacitance=1 FlcProduct=1/5 s^2omegaSquared=5 1/s^2targetOmegaSquared=1 1/s^2candidateOmegaSquared=5 1/s^2tolerance=1 1/s^2distance=4 1/s^2acceptedBit=0 bit