Quantum optical random walk: Quantization rules and quantum simulation of asymptotics
Demosthenes Ellinas, Ioannis Smyrnakis · Physical Review A · 2007
Rules for quantizing the walker-coin parts of a classical random walk are provided by treating them as interacting quantum systems. A quantum optical walk (QOW) is introduced by means of a rule that treats the quantum or classical noise affecting the coin's state as a source of quantization. The long-term asymptotic statistics of the QO walker's position, which shows enhanced diffusion rates as compared to the classical case, is exactly solved. A quantum optical implementation of the walk provides a physical framework for quantum simulation of its asymptotic statistics. The simulation utilizes interacting two-level atoms and/or randomly pulsating laser fields with fluctuating parameters.