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That quantum correlations can be generated over time between the spin and theposition of a quantum walker is indisputable. The creation of bipartiteentanglement has also been reported for two-walker systems. In this scenario,however, since the global state lies in a fourpartite Hilbert space, thequestion arises as to whether genuine multipartite entanglement may develop intime. Also, since the spatial degrees of freedom can be viewed as a noisychannel for the two-spin part, one may wonder how other nonclassical aspects,such as Bell nonlocality, Einstein-Podolsky-Rosen steering, quantum discord,and symmetrical quantum discord, evolve in time during the walk. The lack ofanalytical and numerical evidences which would allow one to address thesequestions is possibly due to the usual computational difficulties associatedwith the recursive nature of quantum walks. Here, we work around this issue byintroducing a simplified Gaussian model which proves to be very accurate withina given domain and powerful for analytical studies. Then, for an instanceinvolving two noninteracting quantum walkers, whose spins start in the singletstate, we quantify the aforementioned nonclassical features as a function oftime, and evaluate violations of both realism and related aspects of locality.In addition, we analyze situations in which the initial two-spin state isaffected by white noise. The typical scenario found is such that while genuinefourpartite entanglement increases over time, all the investigated nonclassicalfeatures vanish (suddenly or asymptotically) except realism-based nonlocality.Moreover, realism is prevented for all finite times. Our findings openperspectives for the understanding of the dynamics of quantum resources inquantum walks.

Nonlocality, quantum correlations, and violations of classical realism in the dynamics of two noninteracting quantum walkers