arXiv subjects

E. Barati

Publications and source records attributed to E. Barati.

4 recordsLinked to original sources

arXiv2011

Generating GHZ state in 2m-qubit spin network

We consider a pure 2m-qubit initial state to evolve under a particular quantum me- chanical spin Hamiltonian, which can be written in terms of the adjacency matrix of the Johnson network J(2m;m). Then, by using some techniques such as spectral dis- tribution and stratification associated with the graphs, employed in [1, 2], a maximally entangled GHZ state is generated between the antipodes of the network. In fact, an explicit formula is given for the suitable coupling strengths of the hamiltonian, so that a maximally entangled state can be generated between antipodes of the network. By using some known multipartite entanglement measures, the amount of the entanglement of the final evolved state is calculated, and finally two examples of four qubit and six qubit states are considered in details.

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arXiv2009

Perfect state transfer of a qudit over underlying networks of group association schemes

As generalizations of results of Christandl et al.\cite{8,9""} and Facer et al.\cite{Facer}, Bernasconi et al.\cite{godsil,godsil1} studied perfect state transfer (PST) between two particles in quantum networks modeled by a large class of cubelike graphs (e.g., the hypercube) which are the Cayley graphs of the elementary abelian group $Z_2^n$. In Refs. \cite{PST,psd}, respectively, PST of a qubit over distance regular spin networks and optimal state transfer (ST) of a $d$-level quantum state (qudit) over pseudo distance regular networks were discussed, where the networks considered there were not in general related with a certain finite group. In this paper, PST of a qudit over antipodes of more general networks called underlying networks of association schemes, is investigated. In particular, we consider the underlying networks of group association schemes in order to employ the group properties (such as irreducible characters) and use the algebraic structure of these networks (such as Bose-Mesner algebra) in order to give an explicit analytical formula for coupling constants in the Hamiltonians so that the state of a particular qudit initially encoded on one site will perfectly evolve to the opposite site without any dynamical control. It is shown that the only necessary condition in order to PST over these networks be achieved is that the centers of the corresponding groups be non-trivial. Therefore, PST over the underlying networks of the group association schemes over all the groups with non-trivial centers such as the abelian groups, the dihedral group $D_{2n}$ with even $n$, the Clifford group CL(n) and all of the $p$-groups can be achieved.

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arXiv2008

Perfect transfer of m-qubit GHZ states

By using some techniques such as spectral distribution and stratification associated with the graphs, employed in [1,2] for the purpose of Perfect state transfer (PST) of a single qubit over antipodes of distance-regular spin networks and PST of a $d$-level quantum state over antipodes of pseudo-distance regular networks, PST of an m-qubit GHZ state is investigated. To do so, we employ the particular distance-regular networks (called Johnson networks) J(2m,m) to transfer an m-qubit GHZ state initially prepared in an arbitrary node of the network (called the reference node) to the corresponding antipode, perfectly. Keywords: Perfect state transferenc, GHZ states, Johnson network, Stratification, Spectral distribution PACs Index: 01.55.+b, 02.10.Yn

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arXiv2008

Perfect transference of a d-level quantum state over pseudo-distance-regular networks

Following the prescription of Ref. \cite{PST} in which perfect state transference (PST) of a qubit over distance regular spin networks was discussed, in this paper PST of an arbitrary $d$-level quantum state (qudit) over antipodes of more general networks called pseudo distance-regular networks, is investigated. In fact, the spectral analysis techniques used in the previous work \cite{PST}, and algebraic structures of pseudo distance-regular graphs are employed to give an explicit formula for suitable coupling constants in the Hamiltonians so that the state of a particular qudit initially encoded on one site will evolve freely to the opposite site without any dynamical control, i.e., we show that how to derive the parameters of the system so that PST can be achieved. Keywords:Perfect state transfer, $d$-level quantum state, Stratification, Pseudo-distance-regular network PACs Index: 01.55.+b, 02.10.Yn

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