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Quantum Information and Measurement (QIM)

Spreading of quantum information through a disordered quantum walk

Farzam Nosrati, Alessandro Laneve, Mahshid Khazaei Shadfar, Andrea Geraldi, Kobra Mahdavipour, Federico Pegoraro, Paolo Matalon, Rosario Lo Franco

Published Jan 1, 2021• 1 citation
Publisher

Abstract

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.
DOI
10.1364/qim.2021.th2a.5

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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.
Summary form only given. In 1958 P.W. Anderson predicted that the wave-function of a quantum particle can be localized in the presence of a static disordered potential [1]. This phenomenon arises from the destructive interference of waves propagating in static disordered media. As a consequence, in these conditions, particle and energy transport through a disordered medium are expected to be strongly suppressed and an initially localized wave packet does not spread out with time. In this work we experimentally study the localization properties of a pair of non-interacting particles obeying bosonic/fermionic statistics by simulating a one-dimensional QW of a two-photon polarization-entangled state in a disordered medium. Quantum walk is the quantum counterpart of classical random walk: a walker jumping between different sites of a lattice with a given probability. In the quantum case the walker is a quantum system, whose quantum properties affect the transport. When multi-particle walkers travel within the QW their bosonic or fermionic nature strongly affects the transport. Here we implement different quantum statistics by exploiting of the polarization-entangled bi-photon input state. The QW circuit has been experimentally realized by femtosecond laser writing which provides a perfect phase stability [2]. In particular, we realized an 8-step quantum walk circuit composed by an array of polarization independent beam splitters arranged in a cascade configuration of Mach-Zehnder (MZ) interferometers (see Fig.1a).
We put forward a versatile and highly scalable experimental setup for the realization of discrete two-dimensional quantum random walks with a single-qubit coin and tunable degree of decoherence. The proposed scheme makes use of a small number of simple optical components arranged in a multipath Mach-Zehnder-like configuration, where a weak coherent state is injected. Environmental effects (decoherence) are generated by a spatial light modulator, which introduces pure dephasing in the transverse spatial plane perpendicular to the direction of propagation of the light beam. By controlling the characteristics of this dephasing, one can explore a great variety of scenarios of quantum random walks: pure quantum evolution (ballistic spread), fast fluctuating environment leading to a diffusive classical random walk, and static disorder resulting in the observation of Anderson localization.