The capability to generate and manipulate quantum states in high-dimensional Hilbert spaces is a crucial step for the development of quantum technologies, from quantum communication to quantum computation. Onedimensional quantum walk dynamics represents a valid tool in the task of engineering arbitrary quantum states.Here we affirm such potential in a linear-optics platform that realizes discrete-time quantum walks in the orbital angular momentum degree of freedom of photons. Different classes of relevant qudit states in a six-dimensional space are prepared and measured, confirming the feasibility of the protocol. Our results represent a further investigation of quantum walk dynamics in photonics platforms, paving the way for the use of such a quantum state-engineering toolbox for a large range of applications.

Quantum state preparation in high-dimensional systems is an essential requirement for many quantumtechnology applications. The engineering of an arbitrary quantum state is, however, typically strongly dependent on the experimental platform chosen for implementation, and a general framework is still missing. Here we show that coined quantum walks on a line, which represent a framework general enough to encompass a variety of different platforms, can be used for quantum state engineering of arbitrary superpositions of the walker's sites. We achieve this goal by identifying a set of conditions that fully characterize the reachable states in the space comprising walker and coin and providing a method to efficiently compute the corresponding set of coin parameters. We assess the feasibility of our proposal by identifying a linear optics experiment based on photonic orbital angular momentum technology.

Quantum state preparation in high-dimensional systems is an essential requirement for many quantum-technology applications. The engineering of an arbitrary quantum state is, however, typically strongly dependent on the experimental platform chosen for implementation, and a general framework is still missing. Here we show that coined quantum walks on a line, which represent a framework general enough to encompass a variety of different platforms, can be used for quantum state engineering of arbitrary superpositions of the walker's sites. We achieve this goal by identifying a set of conditions that fully characterize the reachable states in the space comprising walker and coin, and providing a method to efficiently compute the corresponding set of coin parameters. We assess the feasibility of our proposal by identifying a linear optics experiment based on photonic orbital angular momentum technology.

We address the performance of a coin-biased quantum walk as a generator for non-classical position states of the walker. We exploit a phenomenon of coherent localization in the position space -resulting from the choice of small values of the coin parameter and assisted by post-selection -to engineer large-size coherent superpositions of position states of the walker. The protocol that we design appears to be remarkably robust against both the actual value taken by the coin parameter and strong dephasing-like noise acting on the spatial degree of freedom. We finally illustrate a possible linear-optics implementation of our proposal, suitable for both bulk and integrated-optics platforms.Quantum walks, which generalize the well-known concept of random walks to the quantum domain, have recently attracted considerable attention in light of the possibility that they offer the capability to explore non-trivial phenomena in statistical mechanics [1], such as interference [2], localization [3-6] and tunnelling, and are able to establish entanglement among either the different degrees of freedom of a walker, or the parties of a multi-walker setting [7][8][9][10][11][12][13]. Quantum walk-based architectures for quantum computation have been proposed and theoretically explored [14], while the possibility to implement quantum simulation through schemes based on the dynamics of a quantum walker are currently being pursued both theoretically and experimentally.In the last few years, the number of experimental validations of the quantum walk paradigm, and investigations towards its use for the coherent manipulation of information at the quantum mechanical level have flourished [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. This therefore paves the way to the full exploitation of the possibilities offered by quantum walks for quantum state engineering in Hilbert spaces of large dimensions, which is in general a difficult task to pursue experimentally.In this paper, we explore exactly such a possibility and exploit the statistical features of a discrete-time quantum walk to engineer non-classical states of an N -dimensional system. Specifically, we make use of special coherent localization effects induced on the position state of a quantum walker by choosing properly the operation describing the tossing of a coin. We demonstrate that high-quality coherent superpositions of fully position states © The Author(s) 2018. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.