Decoupled quantum walks, models of the Klein-Gordon and wave equations
1 LIG, Université Joseph Fourier - Grenoble, France
2 Université de Lyon, LIP - 46 allée d'Italie, 69008 Lyon, France
Received: 17 October 2013
Accepted: 19 December 2013
Decoupling a vectorial PDE consists in solving the system for each component, thereby obtaining scalar PDEs that prescribe the evolution of each component independently. We present a general approach to decoupling of Quantum Walks, again defined as a procedure to obtain an evolution law for each scalar component of the Quantum Walks, in such a way that it does not depend on the other components. In particular, the method is applied to show the relation between the Dirac (or Weyl) Quantum Walk in three space dimensions with (or without) mass term, and the Klein-Gordon (or wave) equation.
PACS: 03.67.-a – Quantum information / 03.65.Pm – Relativistic wave equations / 47.11.Qr – Lattice gas
© EPLA, 2013