 This observable has the property that \(\langle \psi, S\phi\rangle = 1\) if \(\ket{\psi}\) and \(\ket{\phi}\) both lie in the same superselection sector as the state in which all the fermions in the measurement device are \(z\)-spin-up. It also has the property that \(\langle\psi,S\phi\rangle = -1\) if they lie in the same superselection sector as the all-down state.  But more interestingly, suppose the target fermion that we want to measure is in a pure superposition of \(z\)-spin-up and \(z\)-spin-down states. Then, after it zips by all the fermions in the measurement device, that measurement device will be left in a superposition of the form \(a\ket{\uparrow} + b\ket{\downarrow}\), where \(\ket{\uparrow}\) is the state in which all the fermions in the device are spin-up and \(\ket{\downarrow}\) is the state in which they are all spin down. Since \(\ket{\uparrow}\) and \(\ket{\downarrow}\) are in different superselection sectors, it follows that their superposition must be a mixed state. In other words, this model allows the measurement device to indicate the pure state of the target fermion, even when that state is a pure superposition, without the device itself being in a pure superposition.