The stationary measure of a space-inhomogeneous three-state quantum walk on the line

详细信息    查看全文

• 作者：Caishi Wang ; Xiangying Lu ; Wenling Wang
• 关键词：Inhomogeneous three ; state quantum walk ; Localization ; Stationary measure ; 60B10 ; 81P45 ; 81P68
• 刊名：Quantum Information Processing
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：14
• 期：3
• 页码：867-880
• 全文大小：172 KB
• 参考文献：1. Aharonov, Y., Davidovich, L., Zagury, N.: Quantum random walks. Phys. Rev. A 48, 1687 (1993) CrossRef
  2. Venegas-Andraca, S.E.: Quantum walks: a comprehensive review. Quantum Inf. Process 11, 1015-106 (2012) CrossRef
  3. Inui, N., Konno, N., Segawa, E.: One-dimensional three-state quantum walk. Phys. Rev. E 72, 056112 (2005). quant-ph/0507207 CrossRef
  4. Inui, N., Konno, N.: Localization of multi-state quantum walk in one dimension. Phys. A 353, 133-44 (2005). quant-ph/0403153 CrossRef
  5. Endo, T., Konno, N.: The stationary measure of a space-inhomogeneous quantum walk on the line. Yohohama Mathematical Journal (in press)? 1309.3054v2 [quant-ph]
  6. Wojcik, A., Luczak, T., Kuraynski, P., Grudka, A., Gdala, T., Bednarska-Bzdega, M.: Trapping a particle of a quantum walk on the line. Phys. Rev. A 85, 012329 (2012) CrossRef
  7. Konno, N., Luczak, T., Segawa, E.: Limit measure of inhomogeneous discrete-time quantum walks in one dimension. Quantum Inf. Process. 12, 33-3 (2013) CrossRef
  8. Konno, N.: The uniform measure for discrete-time quantum walks in one dimension. Quantum Inf. Process. 13, 1103-125 (2014) CrossRef
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Physics
  Mathematics
  Engineering, general
  Computer Science, general
  Characterization and Evaluation Materials
  
• 出版者：Springer Netherlands
• ISSN：1573-1332

文摘

Three-state quantum walks are quite different from two-state quantum walks. Following Endo and Konno (2013), one natural question is: What is the stationary measure of a space-inhomogeneous three-state quantum walk? In this paper, we consider a special space-inhomogeneous three-state quantum walk on the line, which we call the three-state Wojcik walk. We calculate its eigenvalues. And by using the SGF method introduced by Konno et al. (Quantum Inf Pocess 12:35-3, 2013), we obtain its stationary measure. We find that the measure decays exponentially with respect to position under some mild conditions; however, if the walk takes \(-1\) as its eigenvalue, the asymptotic behavior of the measure is independent of position, which contrasts sharply with that of two-state quantum walks.