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New Journal of Physics

Optical implementation of one-dimensional quantum random walks using orbital angular momentum of a single photon

Xu‐Bo Zou, Yuli Dong, Guang‐Can Guo

Published May 30, 2006• 27 citations
Publisher

Abstract

Photons can carry orbital angular momentum (OAM), which offers a practical realization of a high-dimensional quantum information carrier. In this paper, by employing OAM of a single photon, we propose an experimental scheme to implement one-dimensional two-state quantum random walks on an infinite line. Furthermore, we show that the scheme can be used to implement one-dimensional three-state quantum random walks on an infinite line.

DOI
10.1088/1367-2630/8/5/081

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Photons can carry orbital angular momentum (OAM), which offers a practical realization of a high-dimensional quantum information carrier. In this paper, by employing OAM of a single photon, we propose an experimental scheme to implement one-dimensional two-state quantum random walks on an infinite line. Furthermore, we show that the scheme can be used to implement one-dimensional three-state quantum random walks on an infinite line.
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Photons can carry spin angular momentum (SAM) and orbital angular momentum (OAM), which can be used to realize a qubit system and a high-dimension system, respectively. This spin-orbital system is very suitable for implementing one-dimensional discrete-time quantum random walks. We propose a simple scheme of quantum walks on the spin-orbital angular momentum space of photons, where photons walk on the infinite OAM space controlled by their SAM. By employing the recent invention of an optical device, the so-called ``qqq-plate,'' our scheme is more simple and efficient than others because there is no Mach-Zehnder interferometer in the scheme.
A quantum walk is the quantum analog of the classical random walk, which provides a powerful tool for quantum computation and quantum simulation. However, the current experimental realization of the quantum walk based on photonic systems has been restricted to evolution in one dimension or small scale in two dimensions so far, and the growing demands cannot be fulfilled for further application of certain quantum computation tasks. Here, we theoretically propose a feasible scheme of a two-dimensional quantum walk with infinite steps by exploiting the orbital angular momentum of the photons and the phase information of the auxiliary coherent state induced by cross-Kerr nonlinearity. The numerical simulation shows that a proper parameter setting guarantees the walking for infinite steps in a two-dimensional grid with nearly $100\%$100% success probability.
Quantum light sources are one of key devices for quantum information processing, and they are also the important foundation for applications such as in quantum computing, quantum communication, and quantum simulation. Improving the capacity of quantum information coding by using the quantum light source is a major challenge in the development of quantum information technology. Photons with a helical phase front can carry a discrete, unlimited but quantized amount of orbital angular momentum (OAM). The infinite number of states with different OAMs can greatly increase the capacity of optical communication and information processing in quantum regimes. To date photons carrying OAM have mainly been generated by using bulk crystals, which limits the efficiency and the scalability of the source. With the advancement of quantum photonic technology, many significant quantum photonic devices can now be realized on integrated chips. However, creating high-dimensional OAM quantum states at a micro-nano scale is still a challenge. And the research of harnessing high-dimensional OAM mode by using integrated quantum photonic technologies is still in its infancy. Here, the authors review the recent progress and discuss the integrated quantum light sources with OAM. The authors introduce the research progress of using OAM for both single photons and entangled photons and emphasize the exciting work on pushing boundaries in high-dimensional quantum states. This may pave the way for the research and practical applications of high-dimensional quantum light sources.
Abstract Electromagnetic waves have both spin momentum and orbital angular momentum (OAM). Light carrying OAM has broad applications in micro-particle manipulation, high-precision optical metrology, and potential high-capacity optical communications. In the concept of quantum information, a photon encoded with information in its OAM degree of freedom enables quantum networks to carry much more information and increase their channel capacity greatly compared with those of current technology because of the inherent infinite dimensions for OAM. Quantum memories are indispensable to construct quantum networks. Storing OAM states has attracted considerable attention recently, and many important advances in this direction have been achieved during the past few years. Here we review recent experimental realizations of quantum memories using OAM states, including OAM qubits and qutrits at true single photon level, OAM states entangled in a two-dimensional or a high-dimensional space, hyperentanglement and hybrid entanglement consisting of OAM and other degree of freedom in a physical system. We believe that all achievements described here are very helpful to study quantum information encoded in a high-dimensional space.