Quantum information transfer is an important part of quantum information processing. Several proposals for quantum information transfer along linear arrays of nearest-neighbor coupled qubits or spins were made recently. Perfect transfer was shown to exist in two models with specifically designed strongly inhomogeneous couplings. We show that perfect transfer occurs in an entire class of chains, including systems whose nearest-neighbor couplings vary only weakly along the chain. The key to these observations is the Jordan-Wigner mapping of spins to noninteracting lattice fermions which display perfectly periodic dynamics if the single-particle energy spectrum is appropriate. After a half-period of that dynamics any state is transformed into its mirror image with respect to the center of the chain. The absence of fermion interactions preserves these features at arbitrary temperature and allows for the transfer of nontrivially entangled states of several spins or qubits.Quantum information processing (QIP) [1] has been an increasingly important area of physics research over the past decade. The generic building block of QIP is the qubit, which is naturally realized as a spin-1/2 particle. A multitude of coupled spin-1/2 systems have been discussed as possible candidates for the quantum gates needed in quantum computing [2]. Only recently a new focal field of activity has developed, dealing not with the processing, but with the transport of quantum information. As most kinds of directed transport take advantage of one-dimensional structures it seems natural to explore the possibilities of one-dimensional arrays of coupled spin-1/2 systems as transmission lines for quantum information.In [3] a sequence of external RF pulses was proposed to drive single-spin quantum information down a chain of Ising-coupled spins. Other studies proposed to use the natural internal dynamics of coupled spins for the transfer of information. In a homogeneous ferromagnetic Heisenberg chain [4] initially in its ground state, a single-spin state generated at one end of the chain is transferred to the other end with reasonable (but not perfect) fidelity by means of spin waves. This approach is restricted to zero temperature and single spin-wave (and consequently single spin-flip) states since multiple spin-wave states are unstable under the Heisenberg interaction. This excludes the transport of entanglement, except for states of the type α| ↑↓ + β| ↓↑ (with the two spins initially located at fixed sites). The time evolution of these states was studied analytically [5] in an otherwise completely polarized infinitely long ferromagnetic Heisenberg chain. Initial states α| ↑↑ + β| ↓↓ were also studied analytically but with the Heisenberg interaction changed to an XX interaction in order to exclude spin-wave interactions. Spin chain models for single-spin quantum information transport may be implemented as Josephson junction arrays [6]; another proposal [7] involves more general spin networks. Gaussian spin wave packets (i.e. Gaussian weighted su...

We study the dynamics of a single spin 1/2 coupled to a bath of spins 1/2 by inhomogeneous Heisenberg couplings including a central magnetic field. This central-spin model describes decoherence in quantum bit systems. An exact formula for the dynamics of the central spin is presented, based on the Bethe ansatz. For initially completely polarized bath spins and small magnetic field, we find persistent oscillations of the central spin about a nonzero mean value. For a large number of bath spins Nb, the oscillation frequency is proportional to Nb, whereas the amplitude behaves as 1/Nb, to leading order. No asymptotic decay of the oscillations due to the nonuniform couplings is observed, in contrast to some recent studies

The transmission of quantum information between different parts of a quantum computer is of fundamental importance. Spin chains have been proposed as quantum channels for transferring information. Different configurations for the spin couplings were proposed in order to optimize the transfer. As imperfections in the creation of these specific spin-coupling distributions can never be completely avoided, it is important to find out which systems are optimally suited for information transfer by assessing their robustness against imperfections or disturbances. We analyze different spin coupling distributions of spin chain channels designed for perfect quantum state transfer. In particular, we study the transfer of an initial state from one end of the chain to the other end. We quantify the robustness of different coupling distributions against perturbations and we relate it to the properties of the energy eigenstates and eigenvalues. We find that the localization properties of the systems play an important role for robust quantum state transfer.

All eigenstates and eigenvalues are determined for the spin-1 2 XXZ chain Hϭ2J͚ i (S i x S iϩ1for rings with up to Nϭ16 spins, for anisotropies ⌬ϭ0, cos(0.3), and 1. The dynamic spin pair correlations ͗S lϩn (t)S l ͘, (ϭx,z), the dynamic structure factors S (q,), and the intermediate structure factors I (q,t) are calculated for arbitrary temperature T. It is found that for all T, S z (q,) is mainly concentrated on the region ͉͉Ͻ 2 (q), where 2 (q) is the upper boundary of the two-spinon continuum, although excited states corresponding to a much broader frequency spectrum contribute. This is also true for the Haldane-Shastry model and the frustrated Heisenberg model. The intermediate structure factors I (q,t) for ⌬ 0 show exponential decay for high T and large q. Within the accessible time range, the time-dependent spin-correlation functions do not display the long-time signatures of spin diffusion.Approximate analytic expressions for the Tϭ0 dynamic structure factors were conjectured, which take into account known sum rules as well as exact results for the case ⌬ϭ0 and asymptotic results ͑2.5͒ for small q and .

Quantum state transfer in the presence of static disorder and noise is one of the main challenges in building quantum computers. We compare the quantum state transfer properties for two classes of qubit chains under the influence of static disorder. In fully engineered chains all nearest-neighbor couplings are tuned in such a way that a single-qubit state can be transferred perfectly between the ends of the chain, while in chains with modified boundaries only the two couplings between the transmitting and receiving qubits and the remainder of the chain can be optimized. We study how the disorder in the couplings affects the state transfer fidelity depending on the disorder model and strength as well as the chain type and length. We show that the desired level of fidelity and transfer time are important factors in designing a chain. In particular we demonstrate that transfer efficiency comparable or better than that of the most robust engineered systems can also be reached in chains with modified boundaries without the demanding engineering of a large number of couplings.

We calculate exactly the time-dependent reduced density matrix for the central spin in the central-spin model with homogeneous Heisenberg couplings. Therefrom, the dynamics and the entanglement entropy of the central spin are obtained. A rich variety of behaviors is found, depending on the initial state of the bath spins. For an initially unpolarized unentangled bath, the polarization of the central spin decays to zero in the thermodynamic limit, while its entanglement entropy becomes maximal. On the other hand, if the unpolarized environment is initially in an eigenstate of the total bath spin, the central spin and the entanglement entropy exhibit persistent monochromatic large-amplitude oscillations. This raises the question to what extent entanglement of the bath spins prevents decoherence of the central spin.

The dynamics in quantum magnets can often be described by effective models with bosonic excitations obeying a hard-core constraint. Such models can be systematically derived by renormalization schemes such as continuous unitary transformations or by variational approaches. Even in the absence of further interactions the hard-core constraint makes the dynamics of the hard-core bosons nontrivial. Here we develop a systematic diagrammatic approach to the spectral properties of hard-core bosons at finite temperature. Starting from an expansion in the density of thermally excited bosons in a system with an energy gap, our approach leads to a summation of ladder diagrams. Conceptually, the approach is not restricted to one dimension, but the one-dimensional case offers the opportunity to gauge the method by comparison to exact results obtained via a mapping to Jordan-Wigner fermions. In particular, we present results for the thermal broadening of single-particle spectral functions at finite temperature. The line-shape is found to be asymmetric at elevated temperatures and the band-width of the dispersion narrows with increasing temperature. Additionally, the total number of thermally excited bosons is calculated and compared to various approximations and analytic results. Thereby, a flexible approach is introduced which can also be applied to more sophisticated and higher dimensional models.

Over a certain time range the results are free of finite-size effects and thus represent correlation functions of an infinite chain (bulk regime) or a semi-infinite chain (boundary regime). In the bulk regime, the long-time asymptotic decay as inferred by extrapolation is Gaussian at T = oo, exponential at 0 < T < oo, and power-law (~ t-1 1 2 ) at T = 0, in agreement with exact results. In the boundary regime, a power-law decay is obtained at all temperatures; the characteristic exponent is universal at T = 0 (~ r 1 ) and at 0 < T < oo (~ r 3 1 2 ), but is site dependent at T = oo. In the high-temperature regime (T I J ~ 1) and in the low-temperature regime (T I J « 1 ), crossovers between different decay laws can be observed in (Sf(t)Sj). Additional crossovers are found between bulk-type and boundary-type decay for i = j near the boundary, and between spacelike and timelike behavior for i -:f. j.