title: Mimicking the probability distribution of a two-dimensional Grover walk with a single-qubit coin.
abstract: The nonlocalized case of the spatial density probability of the two-dimensional Grover walk can be obtained using only a two-dimensional coin space and a quantum walk in alternate directions. This significantly reduces the resources necessary for its feasible experimental realization. We present a formal proof of this correspondence and analyze the behavior of the coin-position entanglement as well as the x-y spatial entanglement in our scheme with respect to the Grover one. Our scheme allows us to entangle the two orthogonal directions of the walk more efficiently.
authors.affiliation: Department of Physics, University College Cork, Cork, Ireland.
authors.forename: C
authors.initials: C
authors.lastname: Di Franco
authors.forename: M
authors.initials: M
authors.lastname: Mc Gettrick
authors.forename: Th
authors.initials: T
authors.lastname: Busch
mesh_terms: D009717:Numismatics; D011336:Probability; D011789:Quantum Theory; D013269:Stochastic Processes