2002/08/31 by Todd A. Brun, Hilary A. Carteret, Andris Ambainis · 3 citations
Computer Science · Mathematics · Physics and Astronomy · #Classical limit #Heterogeneous random walk in one dimension #Limit (mathematics) #Mathematical analysis #Mathematics #Physics #Position (finance) #Quadratic equation #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum algorithm #Quantum and electron transport phenomena #Quantum decoherence #Quantum mechanics #Quantum walk #Random walk #Statistical physics #Statistics #Variance (accounting) #quant-ph
paper · pdf · doi:10.1103/physrevlett.91.130602
published as Phys. Rev. Lett. 91, 130602 (2003). · 4 pages RevTeX 4.0 + 2 figures (encapsulated Postscript). Trimmed for length. Minor corrections + one new reference
arxiv created 2002/09/20 · openalex publication_date 2003/09/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We look at two possible routes to classical behavior for the discrete quantum random walk on the integers: decoherence in the quantum "coin" which drives the walk, or the use of higher-dimensional (or multiple) coins to dilute the effects of interference. We use the position variance as an indicator of classical behavior and find analytical expressions for this in the long-time limit; we see that the multicoin walk retains the "quantum" quadratic growth of the variance except in the limit of a new coin for every step, while the walk with decoherence exhibits "classical" linear growth of the variance even for weak decoherence.