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| related topics |
| {classical, space, random} |
| {let, theorem, proof} |
| {operator, operators, space} |
| {observables, space, algebra} |
| {measurement, state, measurements} |
| {group, space, representation} |
| {algorithm, log, probability} |
| {field, particle, equation} |
| {vol, operators, histories} |
| {states, state, optimal} |
|
Convergence of coined quantum walks on d-dimensional Euclidean space
Alex D. Gottlieb, Svante Janson, Petra F. Scudo
abstract: Coined quantum walks may be interpreted as the motion in position space of a
quantum particle with a spin degree of freedom; the dynamics are determined by
iterating a unitary transformation which is the product of a spin
transformation and a translation conditional on the spin state. Coined quantum
walks on the d-dimensional lattice can be treated as special cases of coined
quantum walks on d-dimensional Euclidean space. We study quantum walks on
d-dimensional Euclidean space and prove that the sequence of rescaled
probability distributions in position space associated to the unitary evolution
of the particle converges to a limit distribution.
- oai_identifier:
- oai:arXiv.org:quant-ph/0406072
- categories:
- quant-ph
- comments:
- 11 pages
- arxiv_id:
- quant-ph/0406072
- created:
- 2004-06-11
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