Spin Two-State Readout - Physics for Biophysics Step by Step

A spin readout can be modeled as a two-state quantum measurement without drawing an orbiting particle. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Spin readout is a two-state measurement model

The diagram has two possible readout states. It is not a picture of a tiny ball orbiting a nucleus.

\text{two readout states}

Amplitudes set readout probabilities

The probabilities are 9/25 for the first state and 16/25 for the second state.

P_{\text{first}}=\frac{9}{25},\quad P_{\text{second}}=\frac{16}{25}

The two readout probabilities close the budget

The displayed state is the first row. The next rows are limiting cases that show the same two-state budget rule.

\begin{array}{c|c|c}P_{\text{first}}&P_{\text{second}}&\text{total}\\\frac{9}{25}&\frac{16}{25}&1\\1&0&1\\0&1&1\end{array}