Multidimensional quantum diffusions

Germán J. de Valcárcel, Carlo D. Franco, Margarida Hinarejos +4 more

Quantum walks (QWs) are important for quantum information science, but are becoming also interesting for other fields of research as this simple quantum diffusion model finds analogues in diverse physical systems, optical ones in particular. The experimental capabilities regarding QWs have remarkably increased along recent years and several aspects of QWs are now open to experimental research, multidimensional QWs in particular.

R. L. Hudson, Kalyanapuram Rangachari Parthasarathy

Mark W. Coffey, Gabriel G. Colburn

We describe how multidimensional linear diffusion with application to image processing could be carried out on a hybrid classical–quantum computer. We present the quantum-lattice-gas-based algorithms, their effective finite difference approximations and representative simulation results. The methods for two-dimensional diffusion processing are particularly relevant to image enhancement tasks. We additionally demonstrate an extension to constrained linear diffusion that provides for non-uniform image smoothing. The simulation results and accompanying analysis support the utility of both classical and classical–quantum lattice gases for image enhancement. The diffusion modelling has applicability to many other fields including biological and physical science.

VILMA VARCO, JUAN JOSE ESPINOSA

The constancy of the speed of light () in all inertial frames of reference is the foundational postulate of Special Relativity, although its ontological origin remains abstract in classical physics. In this work, we address Lorentz invariance from the framework of Quantum Diffusion (QD) . We propose that the speed limit is not an intrinsic property of objects in extended space , but rather a constraint imposed by the "observation map" that projects multidimensional reality onto accessible 3+1D space. We interpret it as the maximum rate of information propagation allowed by the structure of the ambient coarse-graining . Under this interpretation, Lorentz invariance emerges as a robust symmetry ("pointer state") selected by the environment, guaranteeing that all observers, being constructions of the same reduced state, perceive the same causal update limit.

Mauricio Domingues Coutinho-Neto, Alexandra Viel, Uwe Manthe