Asymptotic properties of the Dirac quantum cellular automaton
arXiv:1504.07418 · doi:10.1103/PhysRevA.93.012328
Abstract
We show that the Dirac quantum cellular automaton [Ann. Phys. 354 (2015) 244] 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, which 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 are similar to the ones achieved by highly localized states of the Dirac equation.
15 pages, 6 figures
References in corpus (16)
- Universal computation by quantum walk
- Quantum Walk in Position Space with Single Optically Trapped Atoms
- Realization of quantum walks with negligible decoherence in waveguide lattices
- A 2D Quantum Walk Simulation of Two-Particle Dynamics
- Discrete single-photon quantum walks with tunable decoherence
- Quantum walks and wavepacket dynamics on a lattice with twisted photons
- Photonic quantum walk in a single beam with twisted light
- Faster quantum walk algorithm for the two dimensional spatial search
- Quantum Walk on a Line with Two Entangled Particles
- Asymptotic evolution of quantum walks with random coin
- Quantum random walk of two photons in separable and entangled state
- Decoherence vs entanglement in coined quantum walks
- Observation of quasiperiodic dynamics in a one-dimensional quantum walk of single photons in space
- Tailoring discrete quantum walk dynamics via extended initial conditions: Towards homogeneous probability distributions
- Chirality asymptotic behavior and non-Markovianity in quantum walks on a line
- Massless Dirac Equation from Fibonacci Discrete-Time Quantum Walk
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