Remote one-qubit state control by pure initial state of two-qubit sender. Selective-region- and eigenvalue-creation

We study the problem of remote one-qubit mixed state creation using a pure initial state of two-qubit sender and spin-1/2 chain as a connecting line. We express the parameters of creatable states in terms of transition amplitudes. We show that the creation of complete receivers state-space can be achieved only in the chain engineered for the one-qubit perfect state transfer (PST) (for instance, in the fully engineered Ekert chain), the chain can be arbitrarily long in this case. As for the homogeneous chain, the creatable receivers state region decreases quickly with the chain length. Both homogeneous chains and chains engineered for PST can be used for the purpose of selective state creation, when only the restricted part of the whole receivers state space is of interest. Among the parameters of the receivers state, the eigenvalue is the most hard creatable one and therefore deserves the special study. Regarding the homogeneous spin chain, an arbitrary eigenvalue can be created only if the chain is of no more then 34 nodes. Alternating chain allows us to increase this length up to 68 nodes.

Robust stationary distributed discord in Jordan-Wigner fermion system under perturbations of initial state

We investigate the Jordan-Wigner fermion clusters with the stationary distributed pairwise quantum discord. Such clusters appear after the Jordan-Wigner transformation of a spin chain governed by the nearest-neighbor XY-Hamiltonian with the particular initial state having one polarized node. We show that the quantum discord stationarity in such systems is not destroyed by the parasitic polarization of at least two types. First type appears because the initial state with a single polarized node is hardly realizable experimentally, so that the low polarization of neighboring nodes must be taken into account. Second, the additional noise-polarization of all nodes is unavoidable. Although the stationarity may not be destroyed by perturbations of the above two types, the parasitic polarizations deform the distribution of the pairwise discord and may destroy the clusters of correlated fermions with equal pairwise discords. Such deformations are studied in this paper.

High probability state transfer in spin-1/2 chains: Analytical and numerical approaches

This article is devoted to the development of analytical and numerical approaches to the problem of the end-to-end quantum state transfer along the spin-1/2 chain using two methods: (a) a homogeneous spin chain with week end bonds and equal Larmor frequencies and (b) a homogeneous spin chain with end Larmor frequencies different from inner ones. A tridiagonal matrix representation of the XY Hamiltonian with nearest neighbor interactions relevant to the quantum state transfer is exactly diagonalized for a combination of the above two methods. In order to take into account interactions of the remote spins we used numerical simulations of the quantum state transfer in ten-node chains. We compare the state transfer times obtained using the two above methods for chains governed by the both XY and XXZ Hamiltonians and using both nearest neighbor and all node interactions.