Sharif Digital Repository

We introduce a simple representation for irreducible spherical tensor operators of the rotation group of arbitrary integer or half integer rank and use these tensor operators to construct matrix product states corresponding to all the variety of valence bond states proposed in the Affleck-Kennedy-Lieb- Tasaki (AKLT) construction. These include the fully dimerized states of arbitrary spins, with uniform or alternating patterns of spins, which are ground states of Hamiltonians with nearest and next-nearest-neighbor interactions, and the partially dimerized or AKLT/valence bond solid states, which are constructed from them by projection. The latter states are translation-invariant ground states... 

We analyze the effect of correlations in a simple model of a small-world network by obtaining exact analytical expressions for the distribution of shortest paths in the network. We enter correlations into a simple model with a distinguished site, by taking the random connections to this site from an Ising distribution. Our method shows how the transfer-matrix technique can be used in the new context of small-world networks. © 2002 The American Physical Society  

We construct a class of quantum channels in arbitrary dimensions for which entanglement improves the performance of the channel. The channels have correlated noise and when the level of correlation passes a critical value we see a sharp transition in the optimal input states (states which minimize the output entropy) from separable to maximally entangled states. We show that for a subclass of channels with some extra conditions, including the examples which we consider, the states which minimize the output entropy are the ones which maximize the mutual information. © 2006 The American Physical Society  

We find exact solutions for a universal set of quantum gates on a scalable candidate for quantum computers, namely an array of two-level systems. The gates are constructed by a combination of dynamical and geometrical (non-Abelian) phases. Previously these gates have been constructed mostly on nonscalable systems and by numerical searches among the loops in the manifold of control parameters of the Hamiltonian. © 2005 The American Physical Society  

Implementation of local quantum gate on specific qubits in an array of qubits by carrying a Hamiltonian around a closed loop is discussed. A family of isospectral Hamiltonians with the same spectrum of the projection operator on the main array is constructed by choice of a suitable curve. For every single qubit gate acting on the k-th qubit, a local operator Xk acts nontrivially on the ancilla and the qubit. Imbedding appropriate operators for a suitable set of qubit gates comprises of a universal set of quantum gates. In tensor product of the array one can enact holonomically any set of gates on any subset of qubits  

It is known that in phase-covariant quantum cloning, the equatorial states on the Bloch sphere can be cloned with a fidelity higher than the optimal bound established for universal quantum cloning. We generalize this concept to include other states on the Bloch sphere with a definite z component of spin. It is shown that once we know the z component, we can always clone a state with a fidelity higher than the universal value and that of equatorial states. We also make a detailed study of the entanglement properties of the output copies and show that the equatorial states are the only states that give rise to a separable density matrix for the outputs. 5555 2002 The American Physical Society  

A one-parameter family of cloning transformation was provided to enable each value of the z component to tune the parameter to obtain the maximum fidelity. It was shown that in this class the equatorial states were the only ones which give rise to a separable density matrix for the outputs. The results given may be useful for those interested in experimental realization of quantum cloning by using nuclear magnetic resonance techniques