New measure of electron correlation

We propose to quantify the "correlation" inherent in a many-electron (or many-fermion) wavefunction by comparing it to the unique uncorrelated state that has the same single-particle density operator as it does.Comment: Final version to appear in PR

Adapting Quality Assurance to Adaptive Systems: The Scenario Coevolution Paradigm

From formal and practical analysis, we identify new challenges that self-adaptive systems pose to the process of quality assurance. When tackling these, the effort spent on various tasks in the process of software engineering is naturally re-distributed. We claim that all steps related to testing need to become self-adaptive to match the capabilities of the self-adaptive system-under-test. Otherwise, the adaptive system's behavior might elude traditional variants of quality assurance. We thus propose the paradigm of scenario coevolution, which describes a pool of test cases and other constraints on system behavior that evolves in parallel to the (in part autonomous) development of behavior in the system-under-test. Scenario coevolution offers a simple structure for the organization of adaptive testing that allows for both human-controlled and autonomous intervention, supporting software engineering for adaptive systems on a procedural as well as technical level.Comment: 17 pages, published at ISOLA 201

Off-diagonal geometric phase for mixed states

We extend the off-diagonal geometric phase [Phys. Rev. Lett. {\bf 85}, 3067 (2000)] to mixed quantal states. The nodal structure of this phase in the qubit (two-level) case is compared with that of the diagonal mixed state geometric phase [Phys. Rev. Lett. {\bf 85}, 2845 (2000)]. Extension to higher dimensional Hilbert spaces is delineated. A physical scenario for the off-diagonal mixed state geometric phase in polarization-entangled two-photon interferometry is proposed.Comment: small corrections; journal reference adde

Generating random density matrices

We study various methods to generate ensembles of random density matrices of a fixed size N, obtained by partial trace of pure states on composite systems. Structured ensembles of random pure states, invariant with respect to local unitary transformations are introduced. To analyze statistical properties of quantum entanglement in bi-partite systems we analyze the distribution of Schmidt coefficients of random pure states. Such a distribution is derived in the case of a superposition of k random maximally entangled states. For another ensemble, obtained by performing selective measurements in a maximally entangled basis on a multi--partite system, we show that this distribution is given by the Fuss-Catalan law and find the average entanglement entropy. A more general class of structured ensembles proposed, containing also the case of Bures, forms an extension of the standard ensemble of structureless random pure states, described asymptotically, as N \to \infty, by the Marchenko-Pastur distribution.Comment: 13 pages in latex with 8 figures include

The geometry of entanglement: metrics, connections and the geometric phase

Using the natural connection equivalent to the SU(2) Yang-Mills instanton on the quaternionic Hopf fibration of $S^7$ over the quaternionic projective space ${\bf HP}^1\simeq S^4$ with an $SU(2)\simeq S^3$ fiber the geometry of entanglement for two qubits is investigated. The relationship between base and fiber i.e. the twisting of the bundle corresponds to the entanglement of the qubits. The measure of entanglement can be related to the length of the shortest geodesic with respect to the Mannoury-Fubini-Study metric on ${\bf HP}^1$ between an arbitrary entangled state, and the separable state nearest to it. Using this result an interpretation of the standard Schmidt decomposition in geometric terms is given. Schmidt states are the nearest and furthest separable ones lying on, or the ones obtained by parallel transport along the geodesic passing through the entangled state. Some examples showing the correspondence between the anolonomy of the connection and entanglement via the geometric phase is shown. Connections with important notions like the Bures-metric, Uhlmann's connection, the hyperbolic structure for density matrices and anholonomic quantum computation are also pointed out.Comment: 42 page

A priori probability that a qubit-qutrit pair is separable

We extend to arbitrarily coupled pairs of qubits (two-state quantum systems) and qutrits (three-state quantum systems) our earlier study (quant-ph/0207181), which was concerned with the simplest instance of entangled quantum systems, pairs of qubits. As in that analysis -- again on the basis of numerical (quasi-Monte Carlo) integration results, but now in a still higher-dimensional space (35-d vs. 15-d) -- we examine a conjecture that the Bures/SD (statistical distinguishability) probability that arbitrarily paired qubits and qutrits are separable (unentangled) has a simple exact value, u/(v Pi^3)= >.00124706, where u = 2^20 3^3 5 7 and v = 19 23 29 31 37 41 43 (the product of consecutive primes). This is considerably less than the conjectured value of the Bures/SD probability, 8/(11 Pi^2) = 0736881, in the qubit-qubit case. Both of these conjectures, in turn, rely upon ones to the effect that the SD volumes of separable states assume certain remarkable forms, involving "primorial" numbers. We also estimate the SD area of the boundary of separable qubit-qutrit states, and provide preliminary calculations of the Bures/SD probability of separability in the general qubit-qubit-qubit and qutrit-qutrit cases.Comment: 9 pages, 3 figures, 2 tables, LaTeX, we utilize recent exact computations of Sommers and Zyczkowski (quant-ph/0304041) of "the Bures volume of mixed quantum states" to refine our conjecture

Tsunami-Related Data: A Review of Available Repositories Used in Scientific Literature

Various organizations and institutions store large volumes of tsunami-related data, whose availability and quality should benefit society, as it improves decision making before the tsunami occurrence, during the tsunami impact, and when coping with the aftermath. However, the existing digital ecosystem surrounding tsunami research prevents us from extracting the maximum benefit from our research investments. The main objective of this study is to explore the field of data repositories providing secondary data associated with tsunami research and analyze the current situation. We analyze the mutual interconnections of references in scientific studies published in the Web of Science database, governmental bodies, commercial organizations, and research agencies. A set of criteria was used to evaluate content and searchability. We identified 60 data repositories with records used in tsunami research. The heterogeneity of data formats, deactivated or nonfunctional web pages, the generality of data repositories, or poor dataset arrangement represent the most significant weak points. We outline the potential contribution of ontology engineering as an example of computer science methods that enable improvements in tsunami-related data management

Induced measures in the space of mixed quantum states

We analyze several product measures in the space of mixed quantum states. In particular we study measures induced by the operation of partial tracing. The natural, rotationally invariant measure on the set of all pure states of a N x K composite system, induces a unique measure in the space of N x N mixed states (or in the space of K x K mixed states, if the reduction takes place with respect to the first subsystem). For K=N the induced measure is equal to the Hilbert-Schmidt measure, which is shown to coincide with the measure induced by singular values of non-Hermitian random Gaussian matrices pertaining to the Ginibre ensemble. We compute several averages with respect to this measure and show that the mean entanglement of $N \times N$ pure states behaves as lnN-1/2.Comment: 12 latex pages, 2 figures in epsf, submited to J. Phys. A. ver.3, some improvements and a few references adde