0000000000056696
AUTHOR
Yasser Omar
Effect of Static Disorder in an Electron-Fabry Perot Interferometr with Two Quantum Scattering Centers
In a recent paper -- F. Ciccarello \emph{et al.}, New J. Phys. \textbf{8}, 214 (2006) -- we have demonstrated that the electron transmission properties of a one-dimensional (1D) wire with two identical embedded spin-1/2 impurities can be significantly affected by entanglement between the spins of the scattering centers. Such effect is of particular interest in the control of transmission of quantum information in nanostructures and can be used as a detection scheme of maximally entangled states of two localized spins. In this letter, we relax the constraint that the two magnetic impurities are equal and investigate how the main results presented in the above paper are affected by a static d…
Entanglement controlled single- electron transmittivity
We consider a system consisting of single electrons moving along a 1D wire in the presence of two magnetic impurities. Such system shows strong analogies with a Fabry - Perot interferometer in which the impurities play the role of two mirrors with a quantum degree of freedom: the spin. We have analysed the electron transmittivity of the wire in the presence of entanglement between the impurity spins. The main result of our analysis is that, for suitable values of the electron momentum, there are two maximally entangled state of the impurity spins the first of which makes the wire transparent whatever the electron spin state while the other strongly inhibits the electron transmittivity. Such…
Spatial Search by Quantum Walk is Optimal for Almost all Graphs.
The problem of finding a marked node in a graph can be solved by the spatial search algorithm based on continuous-time quantum walks (CTQW). However, this algorithm is known to run in optimal time only for a handful of graphs. In this work, we prove that for Erd\"os-Renyi random graphs, i.e.\ graphs of $n$ vertices where each edge exists with probability $p$, search by CTQW is \textit{almost surely} optimal as long as $p\geq \log^{3/2}(n)/n$. Consequently, we show that quantum spatial search is in fact optimal for \emph{almost all} graphs, meaning that the fraction of graphs of $n$ vertices for which this optimality holds tends to one in the asymptotic limit. We obtain this result by provin…
Electron Fabry-Perot interferometer with two entangled magnetic impurities
We consider a one-dimensional (1D) wire along which single conduction electrons can propagate in the presence of two spin-1/2 magnetic impurities. The electron may be scattered by each impurity via a contact-exchange interaction and thus a spin-flip generally occurs at each scattering event. Adopting a quantum waveguide theory approach, we derive the stationary states of the system at all orders in the electron-impurity exchange coupling constant. This allows us to investigate electron transmission for arbitrary initial states of the two impurity spins. We show that for suitable electron wave vectors, the triplet and singlet maximally entangled spin states of the impurities can respectively…
Entanglement generation between two spin-s magnetic impurities in a solid via electron scattering
Abstract We present a scheme for generating entanglement between two magnetic impurities in a solid-state system via electron scattering. The scheme applies to impurities of arbitrary quantum spin number. We show that resonance conditions yield generation of a maximally entangled state of the impurities' spins, regardless of the value of the electron–impurity coupling constant and the impurity spin quantum number. The mechanism behind the scheme is explained in terms of resonance-induced selection rules.
Implementing quantum gates through scattering between a static and a flying qubit
We investigate whether a two-qubit quantum gate can be implemented in a scattering process involving a flying and a static qubit. To this end, we focus on a paradigmatic setup made out of a mobile particle and a quantum impurity, whose respective spin degrees of freedom couple to each other during a one-dimensional scattering process. Once a condition for the occurrence of quantum gates is derived in terms of spin-dependent transmission coefficients, we show that this can be actually fulfilled through the insertion of an additional narrow potential barrier. An interesting observation is that under resonance conditions the above enables a gate only for isotropic Heisenberg (exchange) interac…