Quantum Optical Random Walk: Quantization Rules and Quantum Simulation of Asymptotics

Demosthenes Ellinas † and Ioannis Smyrnakis ‡ Technical University of Crete, Department of Sciences Division of Mathematics, GR 731 00, Chania, Greece. e-mail: † [email protected] ‡ [email protected] Abstract Rules for quantizing the walker+coin parts of a classical random walk are provided by treating them as interacting quantum systems. A quantum optical random walk (QORW), is introduced by means of a new rule that treats quantum or classical noise affecting the coin’s state, as sources of quantization. The long term asymptotic statistics of QORW walker’s position that shows enhanced diffusion rates as compared to classical case, is exactly solved. A quantum optical cavity implementation of the walk provides the framework for quantum simulation of its asymptotic statistics. The simulation utilizes interacting two-level atoms and/or laser randomly pulsating fields with fluctuating parameters.