Discrete randomness in discrete time quantum walk: study via stochastic averaging

Ellinas, D., Bracken, A. J. and Smyrnakis, I. (2012) Discrete randomness in discrete time quantum walk: study via stochastic averaging. Reports On Mathematical Physics, 70 2: 221-227. doi:10.1016/S0034-4877(12)60041-X


Author Ellinas, D.
Bracken, A. J.
Smyrnakis, I.
Title Discrete randomness in discrete time quantum walk: study via stochastic averaging
Journal name Reports On Mathematical Physics   Check publisher's open access policy
ISSN 0034-4877
1879-0674
Publication date 2012-10-01
Year available 2012
Sub-type Article (original research)
DOI 10.1016/S0034-4877(12)60041-X
Volume 70
Issue 2
Start page 221
End page 227
Total pages 7
Place of publication Oxford, United Kingdom
Publisher Pergamon
Language eng
Formatted abstract
The role of classical noise in quantum walks (QW) on integers is investigated in the form of discrete dichotomic random variable affecting its reshuffling matrix parametrized as a SU2)/U (1) coset element. Analysis in terms of quantum statistical moments and generating functions, derived by the completely positive trace preserving (CPTP) map governing evolution, reveals a pronounced eventual transition in walk's diffusion mode, from a quantum ballistic regime with rate O(t) to a classical diffusive regime with rate O(t), when condition (strength of noise parameter) 2 × (number of steps) = 1, is satisfied. The role of classical randomness is studied showing that the randomized QW, when treated on the stochastic average level by means of an appropriate CPTP averaging map, turns out to be equivalent to a novel quantized classical walk without randomness. This result emphasizes the dual role of quantization/randomization in the context of classical random walk
Keyword Quantum walk
Randomness
CP map
Quantization
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2013 Collection
 
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