2015/04/30 by A. Pérez
Computer Science · Mathematics · Physics and Astronomy · #Automaton #Block cellular automaton #Hamiltonian (control theory) #Mathematics #Mobile automaton #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum algorithm #Quantum discord #Quantum entanglement #Quantum mechanics #Quantum walk #Quantum-Dot Cellular Automata #Statistical physics #quant-ph
paper · pdf · doi:10.1103/physreva.93.012328
published as Phys. Rev. A 93, 012328 (2016) · 15 pages, 6 figures
openalex publication_date 2016/01/15 · arxiv created 2016/01/25 · arxiv updated 2016/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We show that the Dirac quantum cellular automaton [A. Bisio, G. M. D'Ariano, and A. Tosini, Ann. Phys. (N.Y.) 354, 244 (2015)] shares many properties in common with the discrete-time quantum walk. These similarities can be exploited to study the automaton as a unitary process that takes place at regular time steps on a one-dimensional lattice, in the spirit of general quantum cellular automata. In this way, it becomes an alternative to the quantum walk, with a dispersion relation that can be controlled by a parameter that plays a similar role to the coin angle in the quantum walk. The Dirac Hamiltonian is recovered under a suitable limit. We provide two independent analytical approximations to the long-term probability distribution. It is shown that, starting from localized conditions, the asymptotic value of the entropy of entanglement between internal and motional degrees of freedom overcomes the known limit that is approached by the quantum walk for the same initial conditions and is similar to the ones achieved by highly localized states of the Dirac equation.