Isotropic quantum walks on lattices and the Weyl equation
Giacomo Mauro D’Ariano, Marco Erba, Paolo Perinotti · Physical Review A · 2017
We present a thorough classification of the isotropic quantum walks on lattices of dimension $d=1,2,3$ with a coin system of dimension $s=2$. For $d=3$ there exist two isotropic walks, namely, the Weyl quantum walks presented in the work of D'Ariano and Perinotti [G. M. D'Ariano and P. Perinotti, Phys. Rev. A 90, 062106 (2014)], resulting in the derivation of the Weyl equation from informational principles. The present analysis, via a crucial use of isotropy, is significantly shorter and avoids a superfluous technical assumption, making the result completely general.