2005/10/19 by Demosthenes Ellinas, Ioannis Smyrnakis · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Asymptotic distribution #Heterogeneous random walk in one dimension #Mathematical analysis #Mathematics #Physics #Probability distribution #Quadratic growth #Quantization (signal processing) #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum algorithm #Quantum mechanics #Quantum walk #Random walk #Statistical physics #Statistics #quant-ph
paper · pdf · doi:10.1016/j.physa.2006.01.008
11 pages, no figures Submitted to Proc. of 3rd NEXT Sigma-Phi, Kolymbari Aug. 2005, Eds. G. Kaniadakis, A. Carbone, M. Lissia
arxiv created 2005/10/19 · openalex publication_date 2006/02/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Quantization and asymptotic behaviour of a variant of discrete random walk on integers are investigated. This variant, the εVk walk, has the novel feature that it uses many identical quantum coins keeping at the same time characteristic quantum features like the quadratically faster than the classical spreading rate, and unexpected distribution cutoffs. A weak limit of the position probability distribution (pd) is obtained, and universal properties of this arch sine asymptotic distribution function are examined. Questions of driving the walk are investigated by means of a quantum optical interaction model that reveals robustness of quantum features of walker's asymptotic pd, against stimulated and spontaneous quantum noise on the coin system.