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We design a quantum probing protocol using quantum walks to investigate the quantum information spreading pattern. We employ quantum Fisher information as a figure of merit to quantify extractable information about an unknown parameter encoded within the quantum walk evolution. Although the approach is universal, we focus on the coherent static and dynamic disorder to investigate anomalous and classical transport as well as Anderson localization. We provide a feasible experimental strategy to implement, in principle, the quantum probing protocol based on the quantum Fisher information using a Mach–Zehnder-like interferometric setup. Our results show that a quantum walk can be considered as a readout device of information about defects and perturbations occurring in complex networks, both classical and quantum.

We propose a quantum probing protocol, a Mach-Zehnder-like interferomet-ric setup, employing quantum walks to explore quantum information spreading patterns, such as anomalous and classical transport, as well as Anderson localization.

We experimentally implemented a controllable inhomogenous Quantum Walk evolution of two photon states. Through the imposition of suitable disorder configurations, we observed an enhance-ment in quantum correlations of the system, compared to the ordered case.

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A witness of non-Markovianity based on the Hilbert–Schmidt speed (HSS), a special type of quantum statistical speed, has been recently introduced for low-dimensional quantum systems. Such a non-Markovianity witness is particularly useful, being easily computable since no diagonalization of the system density matrix is required. We investigate the sensitivity of this HSS-based witness to detect non-Markovianity in various high-dimensional and multipartite open quantum systems with finite Hilbert spaces. We find that the time behaviors of the HSS-based witness are always in agreement with those of quantum negativity or quantum correlation measure. These results show that the HSS-based witness is a faithful identifier of the memory effects appearing in the quantum evolution of a high-dimensional system with a finite Hilbert space.