This tutorial note develops a self-contained engineering-oriented model that connects thecontinuous dynamics of a two-level quantum system to a classical binary readout. The purpose ispedagogical rather than foundational: no new interpretation of quantum mechanics, measurementpostulate, or quantum analog-to-digital conversion protocol is proposed. Instead, establishedelements of open-system dynamics, generalized measurement, stochastic master equations, pointer-state selection, and threshold detection are organized into a single chain that can be simulatedwith conventional state-space tools.A qubit driven by a Hamiltonian H = ℏ(Ωσx + ∆σz )/2 is first described by a Lindbladequation and by the corresponding Bloch equations. Repeated nonselective partial measurementsare represented by a completely positive trace-preserving dephasing channel, from which the exactdiscrete-time coherence decay rate Γϕ = −fs ln (1 − ϵ) is obtained. The distinction between thisensemble-averaged channel and a single experimental realization is then made explicit througha diffusive stochastic master equation. In that conditional description, the detector producesa continuous noisy record; integration over a finite acquisition time and comparison with athreshold yields the final Boolean symbol. The resulting engineering chain is therefore not “wavefunction to bit,” but rather qubit state → detector statistics → analog record → integration →binary decision.Three time scales are emphasized: coherent dynamics, measurement-induced dephasing, andreadout integration. A Nyquist-like sampling inequality is retained only as a temporal-resolutionguideline for ensemble-reconstructed expectation values, not as a sufficient theorem for single-shotquantum-state reconstruction. Finally, the unconditional Bloch equations are mapped ontoan analog state-space macromodel implementable in LTspice. The note includes a correctedreference netlist and a reproducible validation protocol comparing the discrete channel, thecontinuous master equation, averaged stochastic trajectories, and the SPICE realization.
Ricardo Adonis Caraccioli Abrego (Fri,) studied this question.