Distribution of chirality in the quantum walk: Markov process and entanglement
arXiv:1004.1134 · doi:10.1103/PhysRevA.81.062349
Abstract
The asymptotic behavior of the quantum walk on the line is investigated focusing on the probability distribution of chirality independently of position. The long-time limit of this distribution is shown to exist and to depend on the initial conditions, and it also determines the asymptotic value of the entanglement between the coin and the position. It is shown that for given asymptotic values of both the entanglement and the chirality distribution it is possible to find the corresponding initial conditions within a particular class of spatially extended Gaussian distributions. Moreover it is shown that the entanglement also measures the degree of Markovian randomness of the distribution of chirality.
5 pages, 3 figures, It was accepted in Physcial Review A
References in corpus (12)
- Universal computation by quantum walk
- Quantum Walk in Position Space with Single Optically Trapped Atoms
- Photons Walking the Line: A quantum walk with adjustable coin operations
- Realization of quantum walks with negligible decoherence in waveguide lattices
- Discrete single-photon quantum walks with tunable decoherence
- Quantum Walk on a Line with Two Entangled Particles
- A random walk approach to quantum algorithms
- Quantum random walk of two photons in separable and entangled state
- Decoherence vs entanglement in coined quantum walks
- Implementing the one-dimensional quantum (Hadamard) walk using a Bose-Einstein Condensate
- Inhomogeneous Quantum Walks
- Driving quantum walk spreading with the coin operator
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