# Photons walking the line: a quantum walk with adjustable coin operations.

@article{Schreiber2009PhotonsWT, title={Photons walking the line: a quantum walk with adjustable coin operations.}, author={Andreas Schreiber and Katiuscia Nadyne Cassemiro and V{\'a}clav Poto{\vc}ek and Aur{\'e}l G{\'a}bris and Peter J Mosley and Erika Andersson and Igor Jex and Ch. Silberhorn}, journal={Physical review letters}, year={2009}, volume={104 5}, pages={ 050502 } }

We present the first robust implementation of a coined quantum walk over five steps using only passive optical elements. By employing a fiber network loop we keep the amount of required resources constant as the walker's position Hilbert space is increased. We observed a non-Gaussian distribution of the walker's final position, thus characterizing a faster spread of the photon wave packet in comparison to the classical random walk. The walk is realized for many different coin settings and…

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## References

SHOWING 1-10 OF 56 REFERENCES

### Quantum walk of a trapped ion in phase space.

- PhysicsPhysical review letters
- 2009

This work implements the proof of principle for the quantum walk of one ion in a linear ion trap, and proposes an altered protocol based on methods of impulsive steps to scale the quantumWalk to many, in principal to several hundreds of steps.

### Quantum walk on the line as an interference phenomenon

- Physics
- 2003

We show that the coined quantum walk on a line can be understood as an interference phenomenon, can be classically implemented, and indeed already has been. The walk is essentially two independent…

### Quantum random walks and wave-packet reshaping at the single-photon level

- Physics
- 2008

We realize an experimental implementation of one step of a quantum random walk at the single-photon level. After a single step, it is already possible to observe the difference between the quantum…

### Quantum Walk in Position Space with Single Optically Trapped Atoms

- PhysicsScience
- 2009

In this experiment, a quantum walk on the line with single neutral atoms is implemented by deterministically delocalizing them over the sites of a one-dimensional spin-dependent optical lattice and its spatial coherence is demonstrated.

### Quantum walks based on an interferometric analogy

- Physics
- 2003

There are presently two models for quantum walks on graphs. The ''coined'' walk uses discrete-time steps, and contains, besides the particle making the walk, a second quantum system, the coin, that…

### Quantum to classical transition for random walks.

- PhysicsPhysical review letters
- 2003

The position variance is used as an indicator of classical behavior and it is seen that the multicoin walk retains the "quantum" quadratic growth of the variance except in the limit of a new coin for every step, while the walk with decoherence exhibits "classical" linear growth ofThe variance even for weakDecoherence.

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

- Physics
- 2007

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…

### Cyclical Quantum Memory for Photonic Qubits

- Physics
- 2002

We have performed a proof-of-principle experiment in which qubits encoded in the polarization states of single photons from a parametric down-conversion source were coherently stored and read out…

### Recurrence and Pólya number of quantum walks.

- Mathematics, PhysicsPhysical review letters
- 2008

The recurrence probability (Pólya number) is analyzed for d-dimensional unbiased quantum walks and a sufficient condition for a quantum walk to be recurrent is derived and a simple criterion for localization of quantum walks is found.

### Realization of quantum walks with negligible decoherence in waveguide lattices.

- PhysicsPhysical review letters
- 2008

It is shown that the propagation of photons in waveguide lattices, which have been studied extensively in recent years, are essentially an implementation of quantum walks.