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

AbstractCrystalline materials can host topological lattice defects that are robust against local deformations, and such defects can interact in interesting ways with the topological features of the underlying band structure. We design and implement a three dimensional acoustic Weyl metamaterial hosting robust modes bound to a one-dimensional topological lattice defect. The modes are related to topological features of the bulk bands, and carry nonzero orbital angular momentum locked to the direction of propagation. They span a range of axial wavenumbers defined by the projections of two bulk Weyl points to a one-dimensional subspace, in a manner analogous to the formation of Fermi arc surface states. We use acoustic experiments to probe their dispersion relation, orbital angular momentum locked waveguiding, and ability to emit acoustic vortices into free space. These results point to new possibilities for creating and exploiting topological modes in three-dimensional structures through the interplay between band topology in momentum space and topological lattice defects in real space.

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One-dimensional quantum random walks with two entangled coins

Physical Review A ◽

10.1103/physreva.79.032312 ◽

2009 ◽

Vol 79 (3) ◽

Cited By ~ 28

Author(s):

Chaobin Liu ◽

Nelson Petulante

Keyword(s):

Random Walks ◽

Quantum Random Walks ◽

One Dimensional

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Limit theorems and absorption problems for quantum radom walks in one dimension

Quantum Information and Computation ◽

10.26421/qic2.s-7 ◽

2002 ◽

Vol 2 (Special) ◽

pp. 578-595

Author(s):

N. Konno

Keyword(s):

Random Walks ◽

Limit Theorems ◽

The Other ◽

One Dimension ◽

Unitary Matrices ◽

Quantum Random Walks ◽

One Dimensional ◽

The Difference ◽

The One

In this paper we consider limit theorems, symmetry of distribution, and absorption problems for two types of one-dimensional quantum random walks determined by $2 \times 2$ unitary matrices using our PQRS method. The one type was introduced by Gudder in 1988, and the other type was studied intensively by Ambainis et al. in 2001. The difference between both types of quantum random walks is also clarified.

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Implementation of one-dimensional quantum walks on spin-orbital angular momentum space of photons

Physical Review A ◽

10.1103/physreva.81.052322 ◽

2010 ◽

Vol 81 (5) ◽

Cited By ~ 30

Author(s):

Pei Zhang ◽

Bi-Heng Liu ◽

Rui-Feng Liu ◽

Hong-Rong Li ◽

Fu-Li Li ◽

...

Keyword(s):

Angular Momentum ◽

Orbital Angular Momentum ◽

Momentum Space ◽

Quantum Walks ◽

Spin Orbital ◽

One Dimensional

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Quantum random walks in one dimension via generating functions

Discrete Mathematics & Theoretical Computer Science ◽

10.46298/dmtcs.3533 ◽

2007 ◽

Vol DMTCS Proceedings vol. AH,... (Proceedings) ◽

Author(s):

Andrew Bressler ◽

Robin Pemantle

Keyword(s):

Random Walks ◽

Generating Functions ◽

Nearest Neighbor ◽

Function Analysis ◽

One Dimension ◽

Quantum Random Walks ◽

Linear Speed ◽

One Dimensional ◽

Asymptotic Term ◽

International Audience

International audience We analyze nearest neighbor one-dimensional quantum random walks with arbitrary unitary coin-flip matrices. Using a multivariate generating function analysis we give a simplified proof of a known phenomenon, namely that the walk has linear speed rather than the diffusive behavior observed in classical random walks. We also obtain exact formulae for the leading asymptotic term of the wave function and the location probabilities.

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INTERACTING FOCK SPACES AND THE MOMENTS OF THE LIMIT DISTRIBUTIONS FOR QUANTUM RANDOM WALKS

Infinite Dimensional Analysis Quantum Probability and Related Topics ◽

10.1142/s0219025713500033 ◽

2013 ◽

Vol 16 (01) ◽

pp. 1350003 ◽

Cited By ~ 2

Author(s):

CHUL KI KO ◽

HYUN JAE YOO

Keyword(s):

Spectral Analysis ◽

Random Walks ◽

Vacuum Expectation ◽

High Dimensional ◽

Fock Spaces ◽

Quantum Random Walks ◽

One Dimensional ◽

Limit Distributions ◽

Time Quantum ◽

Adjoint Operators

We investigate the limit distributions of the discrete time quantum random walks on lattice spaces via a spectral analysis of concretely given self-adjoint operators. We discuss the interacting Fock spaces associated with the limit distributions. Thereby, we represent the moments of the limit distribution by vacuum expectation of the monomials of the Fock operator. We get formulas not only for one-dimensional walks but also for high-dimensional walks.

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