Interference and correlated coherence in disordered and localized quantum walk
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Abstract
Quantum walk has played an important role in development of quantum algorithms and protocols for quantum simulations. The speedup observed in quantum walk algorithms is attributed to quantum interference of spreading wave packet in position space. Similarly, localization in quantum walk due to disorder is also attributed to quantum interference effect. Therefore, it is intriguing to have a closer look and understand the way quantum interference manifests in different forms of quantum walk dynamics. Here we will use interference measure to quantify the interference in position space and coin space, together and independently. This interference measure helps us to differentiate localisation seen in quantum walks due to different forms of disorder and topological effects. We also shown that the interference measure in the coin space alone can serve as an indicator of the spatially localized quantum state. Comparing the result of interference and correlated coherence with the entanglement dynamics we show that all the intricate features of entanglement is captured by correlated coherence. This will give us a better understanding of role of quantum interference in quantum dynamics and its effect on entanglement. With the control over quantum walk dynamics and quantum interference, exploring the possibility of using interference as resource will be of immediate interest.