Teleportation of an Arbitrary Multipartite GHZ-Class State by One EPR Pair

We present a scheme for perfectly teleporting an arbitrary and unknown N-particle GHZ-class state from a sender to a receiver. We just need one quantum channel composed of two or three particles in the maximally entangled state. The sender performs one Bell-state measurement on two of her particles and N - 1 Hadamard operations and N - 1 yon Neumann measurements on the rest N - 1 particles. The receiver adopts one corresponding unitary transformation on his particles shared with the sender. After that, the receiver can obtain the original N-particle GHZ-class state by introducing N - 1 ancillary particles and carrying out N - 1 controlled-NOT operations. We also generalize the scheme to the case of controlled teleportation.     

Bias of the structural quasi-score estimator of a measurement error model under misspecification of the regressor distribution

In a structural measurement error model the structural quasi-score (SQS) estimator is based on the distribution of the latent regressor variable. If this distribution is misspecified, the SQS estimator is (asymptotically) biased. Two types of misspecification are considered. Both assume that the statistician erroneously adopts a normal distribution as his model for the regressor distribution. In the first type of misspecification, the true model consists of a mixture of normal distributions which cluster around a single normal distribution, in the second type, the true distribution is a normal distribution admixed with a second normal distribution of low weight. In both cases of misspecification, the bias, of course, tends to zero when the size of misspecification tends to zero. However, in the first case the bias goes to zero in a flat way so that small deviations from the true model lead to a negligible bias, whereas in the second case the bias is noticeable even for small deviations from the true model.     

Infima and complements in the lattice of quasi-uniformities

We show that the infimum of any family of proximally symmetric quasi-uniformities is proximally symmetric, while the supremum of two proximally symmetric quasi-uniformities need not be proximally symmetric. On the other hand, the supremum of any family of transitive quasi-uniformities is transitive, while there are transitive quasi-uniformities whose infimum with their conjugate quasi-uniformity is not transitive. Moreover we present two examples that show that neither the supremum topology nor the infimum topology of two transitive topologies need be transitive. Finally, we prove that several operations one can perform on and between quasi-uniformities preserve the property of having a complement.     

Single Qubit and Its Universal Logic Gate Made of a Heisenberg Spin Cluster with Five Particles

We investigate an anisotropic Heisenberg spin cluster with five particles controlled by a time-dependent magnetic field. With the algebraic dynamical method, we obtain the exact analytical solution to the time dependent Schr6dinger equation. Based on the analytical solution, it is shown that the system can be used as a universal single qubit logic gate controlled by the strength and frequency of the magnetic field, and the six special single qubit logic gates can be realized physically. We also discuss the anti-decoherence property of the qubit and its logic gates resulted from particle coupling effect and collectivity of the cluster.     

Tropical Weyl Group Action via Point Configurations and τ-Functions of the q-Painlevé Equations

Starting from certain point sets in the projective plane, we construct a tropical (or subtraction-free birational) representation of Weyl groups over the field of τ-functions. In particular, our construction includes E ₈ ⁽¹⁾ , E ₇ ⁽¹⁾ , E ₆ ⁽¹⁾ and D ₅ ⁽¹⁾ as affine cases; each of them gives rise to the q-difference Painlevé equation.     

Normal Bundles to Laufer Rational Curves in Local Calabi–Yau Threefolds

We prove a conjecture by F. Ferrari. Let X be the total space of a nonlinear deformation of a rank two holomorphic vector bundle on a smooth rational curve, such that X has trivial canonical bundle and has sections. Then the normal bundle to such sections is computed in terms of the rank of the Hessian of a suitably defined superpotential at its critical points.     

Coalgebraic representations of distributive lattices with operators

We present a framework for extending Stone's representation theorem for distributive lattices to representation theorems for distributive lattices with operators. We proceed by introducing the definition of algebraic theory of operators over distributive lattices. Each such theory induces a functor on the category of distributive lattices such that its algebras are exactly the distributive lattices with operators in the original theory. We characterize the topological counterpart of these algebras in terms of suitable coalgebras on spectral spaces. We work out some of these coalgebraic representations, including a new representation theorem for distributive lattices with monotone operators.     

Nonminimal sets,their projections and integral representations of stable processes

New criteria are provided for determining whether an integral representation of a stable process is minimal. These criteria are based on various nonminimal sets and their projections, and have several advantages over and shed light on already available criteria. In particular, they naturally lead from a nonminimal representation to the one which is minimal. Several known examples are considered to illustrate the main results. The general approach is also adapted to show that the so-called mixed moving averages have a minimal integral representation of the mixed moving average type.     

Symmetric incidence groupoids

In [7] point-reflection geometries were studied which can be derived from commutative kinematic spaces without involutory elements. But the class of point-reflection geometries is larger. For example, elliptic planes with their reflections cannot be derived from commutative kinematic spaces. Here we investigate a larger class of reflection geometries.This paper was sponsored by Vigoni Program 1999.