Quantum Computation and Communication with Qubit Systems

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54 3. Quantum communication in quantum networks Figure 3.1: This figure depicts the possibility of transporting quantum information from one quantum processor to another through a line of stationary qubits. that describes the total energy of the system (see appendix for further details), for the interaction between the ith and the jth spin is written as H XYZ ij =J ij null S i . null S j , (3.1) where null S i . null S j ≡S x i S x j +S y i S y j +S z i S z j andS x i ,S y i ,S z i aretheoperatorsforthecomponentof theith spin along thex,y and z directions respectively andJ ij is the coupling constant between two interacting spins (normalized to 1). In particular, when all the spins form spin-half systems, S x ,S y and S z stand for the familiar Pauli matrices σ x ,σ y and σ z . A Hamiltonian of the above form is termed as exchange interaction as it can arise in from the pure exchange of electrons between neighbor ions in a metal (details can be found in appendix). It is also called the Heisenberg interaction after the name of the scientist who studied this kind of interaction. In particular, the specific Hamiltonian we have written above is called the isotropic exchange interaction because the interactions are considered along the three Euclidean axes. Later on, we will also encounter a variant of the above interaction H XY ij =J ij (S x i S x j +S y i S y j ), (3.2) which is called the XY interaction. We will be primarily concerned with chains and networks of interacting spin-half systems in this thesis. A graphic representations of such systems is shown in Fig.3.2

Anteprima della Tesi di Andrea Casaccino

Anteprima della tesi: Quantum Computation and Communication with Qubit Systems, Pagina 3

Tesi di Dottorato

Dipartimento: Ingegneria dell' Informazione

Autore: Andrea Casaccino Contatta »

Composta da 166 pagine.

 

Questa tesi ha raggiunto 148 click dal 11/03/2011.

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