Figure 3

(a) State fidelity between the position state of the walker at the end of a \(\pmb{2N+1}\)-site walk (obtained by tracing away the coin’s degrees of freedom) with \(\pmb{\theta=\pi/40}\) (initial state \(\pmb{\vert {0} \rangle_{p}\otimes \vert {\phi} \rangle_{c}}\)) and a coherent superposition states of the form \(\pmb{(\vert {-N+k} \rangle\pm \vert {N-k} \rangle)/\sqrt{2}}\). We have considered the cases of \(k=0\) (blue, top curve), \(k=1\) (red, middle curve), and \(k=2\) (green, bottom curve). (b) Same as panel (a) but for \(\theta=\pi/100\). (c) and (d) Same analysis as in panels (a) and (b), respectively, but for a conditional position state achieved by projecting the coin onto \(\vert {\phi} \rangle_{c}\) at the end of the walk.