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arXiv · 1708.00826

Isotropic quantum walks on lattices and the Weyl equation

Giacomo Mauro D'Ariano·Marco Erba·Paolo Perinotti
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Abstract

We present a thorough classification of the isotropic quantum walks on lattices of dimension $d=1,2,3$ for cell dimension $s=2$. For $d=3$ there exist two isotropic walks, namely the Weyl quantum walks presented in Ref. [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.

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Giacomo Mauro D'Ariano, Marco Erba, Paolo Perinotti. 2017-08-02. Isotropic quantum walks on lattices and the Weyl equation. https://doi.org/10.1103/physreva.96.062101

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