2012/01/23 by André Ahlbrecht, Andre Ahlbrecht, Christopher Cedzich +5 · 3 citations
Computer Science · Mathematics · Physics and Astronomy · #Applied mathematics #Degenerate energy levels #Gaussian #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum and electron transport phenomena #Quantum computer #Quantum decoherence #Quantum mechanics #Quantum walk #Random walk #Randomness #Statistical physics #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1007/s11128-012-0389-4
published as Quantum Information Processing 11, 1219 (2012)
arxiv created 2012/01/23 · openalex publication_date 2012/03/24 · arxiv updated 2015/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Quantum walks subject to decoherence generically suffer the loss of their genuine quantum feature, a quadratically faster spreading compared to classical random walks. This intuitive statement has been verified analytically for certain models and is also supported by numerical studies of a variety of examples. In this paper we analyze the long-time behavior of a particular class of decoherent quantum walks, which, to the best of our knowledge, was only studied at the level of numerical simulations before. We consider a local coin operation which is randomly and independently chosen for each time step and each lattice site and prove that, under rather mild conditions, this leads to classical behavior: With the same scaling as needed for a classical diffusion the position distribution converges to a Gaussian, which is independent of the initial state. Our method is based on non-degenerate perturbation theory and yields an explicit expression for the covariance matrix of the asymptotic Gaussian in terms of the randomness parameters.