Emergence of Randomness and Arrow of Time in Quantum Walks

Abstract

Quantum walks are powerful tools not only to construct the quantum speedup algorithms but also to describe specific models in physical processes. Furthermore, the discrete time quantum walk has been experimentally realized in various setups. We apply the concept of the quantum walk to the problems in quantum foundations. We show that randomness and the arrow of time in the quantum walk gradually emerge by periodic projective measurements from the mathematically obtained limit distribution under the time scale transformation.

6 pages, 3 figures

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• Asymptotic evolution of quantum walks with random coin
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• Entanglement engineering and topological protection by discrete-time quantum walks
• Experimental simulation and limitations of quantum walks with trapped ions
• Survival probability in a one-dimensional quantum walk on a trapped lattice
• Crossovers induced by discrete-time quantum walks
• Photonic Discrete-time Quantum Walks and Applications
• Quantum walks: decoherence and coin-flipping games
• Asymptotic evolution of quantum walks on the $N$-cycle subject to decoherence on both the coin and position degrees of freedom
• Classical-like behavior in quantum walks with inhomogeneous, time-dependent coin operators
• Entropy rate of message sources driven by quantum walks
• Framework for discrete-time quantum walks and a symmetric walk on a binary tree
• Scaling and crossover behaviour in a truncated long range quantum walk
• Non-Hermitian and Zeno limit of quantum systems under rapid measurements
• Massless Dirac Equation from Fibonacci Discrete-Time Quantum Walk
• Topology, Holonomy, and Quantum Walks
• Observation of Topological Structures in Photonic Quantum Walks
• Quantum Walk Topology and Spontaneous Parametric Down Conversion
• Quantum Walks with Non-Orthogonal Position States
• Weak limit theorem of a two-phase quantum walk with one defect
• Localization and Fractality in Inhomogeneous Quantum Walks with Self-Duality