 where the subscripts 0, 1, and 2 indicate the time. In words, what tells us is that if at the end of a run the pointer is in position \(k\), then at the earlier time before the measurement took place the particle had a property represented by a projector \(\xi^{jk}\) for some value of \(j\). If in addition the initial state \({|s_0\rangle }\) is known, that can be used to assign a probability \(p_{jk}\), note that \(\sum_j p_{jk}=1\), to the property \(\xi^{jk}\) at time \(t_1\). While not as “clean” as in the case of a projective measurement, this can still be informative.