scholarly journals One-dimensional quantum random walks with two entangled coins

2009 ◽  
Vol 79 (3) ◽  
Author(s):  
Chaobin Liu ◽  
Nelson Petulante
Keyword(s):  
Random Walks ◽  
Quantum Random Walks ◽  
One Dimensional

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

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.

scholarly journals Quantum random walks in one dimension via generating functions

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.

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

2007 ◽  
Vol 75 (5) ◽  
Author(s):  
Pei Zhang ◽  
Xi-Feng Ren ◽  
Xu-Bo Zou ◽  
Bi-Heng Liu ◽  
Yun-Feng Huang ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Random Walks ◽  
Orbital Angular Momentum ◽  
Quantum Random Walks ◽  
One Dimensional

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

2013 ◽  
Vol 16 (01) ◽  
pp. 1350003 ◽  
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.

Computer Simulations for Some One-Dimensional Models of Random Walks in Fluctuating Random Environment

2005 ◽  
Vol 121 (3-4) ◽  
pp. 361-372 ◽  
Author(s):  
C. Boldrighini ◽  
G. Cosimi ◽  
S. Frigio ◽  
A. Pellegrinotti
Keyword(s):  
Random Walks ◽  
Computer Simulations ◽  
Random Environment ◽  
One Dimensional ◽  
Dimensional Models

On coupling of random walks and renewal processes

1996 ◽  
Vol 33 (1) ◽  
pp. 122-126
Author(s):  
Torgny Lindvall ◽  
L. C. G. Rogers
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Simple Random Walk ◽  
Renewal Processes ◽  
Renewal Theorem ◽  
One Dimensional ◽  
Continuous State Space ◽  
Continuous State ◽  
Efficient Coupling ◽  
Blackwell's Renewal Theorem

The use of Mineka coupling is extended to a case with a continuous state space: an efficient coupling of random walks S and S' in can be made such that S' — S is virtually a one-dimensional simple random walk. This insight settles a zero-two law of ergodicity. One more proof of Blackwell's renewal theorem is also presented.

scholarly journals One dimensional quantum walks with memory

2010 ◽  
Vol 10 (5&6) ◽  
pp. 509-524
Author(s):  
M. Mc Gettrick
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Random Walks ◽  
Quantum Walks ◽  
One Dimensional ◽  
With Memory ◽  
Previous Step

We investigate the quantum versions of a one-dimensional random walk, whose corresponding Markov Chain is of order 2. This corresponds to the walk having a memory of one previous step. We derive the amplitudes and probabilities for these walks, and point out how they differ from both classical random walks, and quantum walks without memory.

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