Entanglement versus Correlations in Spin Systems

We consider pure quantum states of $N\gg 1$ spins or qubits and study the average entanglement that can be \emph{localized} between two separated spins by performing local measurements on the other individual spins. We show that all classical correlation functions provide lower bounds to this \emph{localizable entanglement}, which follows from the observation that classical correlations can always be increased by doing appropriate local measurements on the other qubits. We analyze the localizable entanglement in familiar spin systems and illustrate the results on the hand of the Ising spin model, in which we observe characteristic features for a quantum phase transition such as a diverging entanglement length.Comment: 4 page

Developing the Deutsch-Hayden approach to quantum mechanics

The formalism of Deutsch and Hayden is a useful tool for describing quantum mechanics explicitly as local and unitary, and therefore quantum information theory as concerning a "flow" of information between systems. In this paper we show that these physical descriptions of flow are unique, and develop the approach further to include the measurement interaction and mixed states. We then give an analysis of entanglement swapping in this approach, showing that it does not in fact contain non-local effects or some form of superluminal signalling.Comment: 14 pages. Added section on entanglement swappin

Dynamic quantum clustering: a method for visual exploration of structures in data

A given set of data-points in some feature space may be associated with a Schrodinger equation whose potential is determined by the data. This is known to lead to good clustering solutions. Here we extend this approach into a full-fledged dynamical scheme using a time-dependent Schrodinger equation. Moreover, we approximate this Hamiltonian formalism by a truncated calculation within a set of Gaussian wave functions (coherent states) centered around the original points. This allows for analytic evaluation of the time evolution of all such states, opening up the possibility of exploration of relationships among data-points through observation of varying dynamical-distances among points and convergence of points into clusters. This formalism may be further supplemented by preprocessing, such as dimensional reduction through singular value decomposition or feature filtering.Comment: 15 pages, 9 figure

StemNet: An Evolving Service for Knowledge Networking in the Life Sciences

Up until now, crucial life science information resources, whether bibliographic or factual databases, are isolated from each other. Moreover, semantic metadata intended to structure their contents is supplied in a manual form only. In the StemNet project we aim at developing a framework for semantic interoperability for these resources. This will facilitate the extraction of relevant information from textual sources and the generation of semantic metadata in a fully automatic manner. In this way, (from a computational perspective) unstructured life science documents are linked to structured biological fact databases, in particular to the identifiers of genes, proteins, etc. Thus, life scientists will be able to seamlessly access information from a homogeneous platform, despite the fact that the original information was unlinked and scattered over the whole variety of heterogeneous life science information resources and, therefore, almost inaccessible for integrated systematic search by academic, clinical, or industrial users

Spectral Conditions on the State of a Composite Quantum System Implying its Separability

For any unitarily invariant convex function F on the states of a composite quantum system which isolates the trace there is a critical constant C such that F(w)<= C for a state w implies that w is not entangled; and for any possible D > C there are entangled states v with F(v)=D. Upper- and lower bounds on C are given. The critical values of some F's for qubit/qubit and qubit/qutrit bipartite systems are computed. Simple conditions on the spectrum of a state guaranteeing separability are obtained. It is shown that the thermal equilbrium states specified by any Hamiltonian of an arbitrary compositum are separable if the temperature is high enough.Comment: Corrects 1. of Lemma 2, and the (under)statement of Proposition 7 of the earlier version

Singular value decomposition and matrix reorderings in quantum information theory

We review Schmidt and Kraus decompositions in the form of singular value decomposition using operations of reshaping, vectorization and reshuffling. We use the introduced notation to analyse the correspondence between quantum states and operations with the help of Jamiolkowski isomorphism. The presented matrix reorderings allow us to obtain simple formulae for the composition of quantum channels and partial operations used in quantum information theory. To provide examples of the discussed operations we utilize a package for the Mathematica computing system implementing basic functions used in the calculations related to quantum information theory.Comment: 11 pages, no figures, see http://zksi.iitis.pl/wiki/projects:mathematica-qi for related softwar