A New Type of Limit Theorems for the One-Dimensional Quantum Random Walk
| dc.creator | Konno, Norio | |
| dc.date | 2002-06-17 | |
| dc.date | 2005-11-01 | |
| dc.date.accessioned | 2026-07-07T06:36:25Z | |
| dc.date.available | 2026-07-07T06:36:25Z | |
| dc.description | In this paper we consider the one-dimensional quantum random walk X^{varphi} _n at time n starting from initial qubit state varphi determined by 2 times 2 unitary matrix U. We give a combinatorial expression for the characteristic function of X^{varphi}_n. The expression clarifies the dependence of it on components of unitary matrix U and initial qubit state varphi. As a consequence of the above results, we present a new type of limit theorems for the quantum random walk. In contrast with the de Moivre-Laplace limit theorem, our symmetric case implies that X^{varphi}_n /n converges in distribution to a limit Z^{varphi} as n to infty where Z^{varphi} has a density 1 / pi (1-x^2) sqrt{1-2x^2} for x in (- 1/sqrt{2}, 1/sqrt{2}). Moreover we discuss some known simulation results based on our limit theorems. | |
| dc.description | Final version; Journal-ref added; 14 pages; this arXiv version has no figures | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0206103 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0206103 | |
| dc.identifier | Journal of the Mathematical Society of Japan, Vol.57, No.4, pp.1179-1195 (2005) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/100072 | |
| dc.subject | Quantum Physics | |
| dc.title | A New Type of Limit Theorems for the One-Dimensional Quantum Random Walk | |
| dc.type | text |