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Physical Review A

Demonstration of one-dimensional quantum random walks using orbital angular momentum of photons

Pei Zhang, Xi‐Feng Ren, Xu‐Bo Zou, Bi‐Heng Liu, Yun‐Feng Huang, Guang‐Can Guo

Published May 9, 2007• 63 citations
Publisher

Abstract

Quantum random walks have attracted special interest because they could lead to new quantum algorithms. Photons can carry orbital angular momentum (OAM) thereby offering a practical realization of a high-dimensional quantum information carrier. By employing OAM of photons, we experimentally realized the one-dimensional discrete-time quantum random walk. Three steps of a one-dimensional quantum random walk were implemented in our protocol showing the obvious difference between quantum and classical random walks.

DOI
10.1103/physreva.75.052310

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Quantum random walks have attracted special interest because they could lead to new quantum algorithms. Photons can carry orbital angular momentum (OAM) thereby offering a practical realization of a high-dimensional quantum information carrier. By employing OAM of photons, we experimentally realized the one-dimensional discrete-time quantum random walk. Three steps of a one-dimensional quantum random walk were implemented in our protocol showing the obvious difference between quantum and classical random walks.
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 walks. Despite their simple structure they form a universal platform to implement any algorithm of quantum computation. However, it is very hard to realize quantum walks with a sufficient number of iterations in quantum systems due to their sensitivity to environmental influences and subsequent loss of coherence. Here we present a scalable implementation scheme for one-dimensional quantum walks for arbitrary number of steps using the orbital angular momentum modes of classical light beams. Furthermore, we show that using the same setup with a minor adjustment we can also realize electric quantum walks.
Among all degrees of freedom offered by single photons, the orbital angular momentum (OAM) has a great potential in the quantum information field, as it provides a natural choice for implementing single-photon qudits, the units of quantum information in a higher dimensional space. This can be an important practical advantage, as it enables higher security in quantum cryptographic protocols, as well as implications in fundamental quantum mechanics theory. Moreover, the combined use of different degrees of freedom of a photon, such as OAM and spin, enables the implementation of entirely new quantum tasks.
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. One-dimensional 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.