Geometric Effects and Computation in Spin Networks

When initially introduced, a Hamiltonian that realises perfect transfer of a quantum state was found to be analogous to an x-rotation of a large spin. In this paper we extend the analogy further to demonstrate geometric effects by performing rotations on the spin. Such effects can be used to determine properties of the chain, such as its length, in a robust manner. Alternatively, they can form the basis of a spin network quantum computer. We demonstrate a universal set of gates in such a system by both dynamical and geometrical means

Injury Risk Estimation Expertise Assessing the ACL Injury Risk Estimation Quiz

Background: Available methods for screening anterior cruciate ligament (ACL) injury risk are effective but limited in application as they generally rely on expensive and time-consuming biomechanical movement analysis. A potential efficient alternative to biomechanical screening is skilled movement analysis via visual inspection (ie, having experts estimate injury risk factors based on observations of athletes’ movements). Purpose: To develop a brief, valid psychometric assessment of ACL injury risk factor estimation skill: the ACL Injury Risk Estimation Quiz (ACL-IQ). Study Design: Cohort study (diagnosis); Level of evidence, 3. Methods: A total of 660 individuals participated in various stages of the study, including athletes, physicians, physical therapists, athletic trainers, exercise science researchers/students, and members of the general public in the United States. The ACL-IQ was fully computerized and made available online (www.ACL-IQ.org). Item sampling/reduction, reliability analysis, cross-validation, and convergent/discriminant validity analysis were conducted to optimize the efficiency and validity of the assessment. Results: Psychometric optimization techniques identified a short (mean time, 2 min 24 s), robust, 5-item assessment with high reliability (test-retest: r = 0.90) and consistent discriminability (average difference of exercise science professionals vs general population: Cohen d = 1.98). Exercise science professionals and general population individuals scored 74% and 53% correct, respectively. Convergent and discriminant validity was demonstrated. Scores on the ACL-IQ were most associated with ACL knowledge and various cue utilities and were least associated with domain-general spatial/decision-making ability, personality, or other demographic variables. Overall, 23% of the total sample (40% exercise science professionals; 6% general population) performed better than or equal to the ACL nomogram. Conclusion: This study presents the results of a systematic approach to assess individual differences in ACL injury risk factor estimation skill; the assessment approach is efficient (ie, it can be completed in\3 min) and psychometrically robust. The results provide evidence that some individuals have the ability to visually estimate ACL injury risk factors more accurately than other instrument-based ACL risk estimation methods (ie, ACL nomogram). The ACL-IQ provides the foundation for assessing the efficacy of observational ACL injury risk factor assessment (ie, does simple skilled visual inspection reduce ACL injuries?). It also provides a representative task environment that can be used to increase our understanding of the perceptual-cognitive mechanisms underlying observational movement analysis and to improve injury risk assessment performance

Scaling of the low temperature dephasing rate in Kondo systems

We present phase coherence time measurements in quasi-one-dimensional Ag wires doped with Fe Kondo impurities of different concentrations $n_s$. Due to the relatively high Kondo temperature $T_{K}\approx 4.3K$ of this system, we are able to explore a temperature range from above $T_{K}$ down to below $0.01 T_{K}$. We show that the magnetic contribution to the dephasing rate $\gamma_m$ per impurity is described by a single, universal curve when plotted as a function of $(T/T_K)$. For $T>0.1 T_K$, the dephasing rate is remarkably well described by recent numerical results for spin $S=1/2$ impurities. At lower temperature, we observe deviations from this theory. Based on a comparison with theoretical calculations for $S>1/2$, we discuss possible explanations for the observed deviations.Comment: 4 pages, 3 figures, submitted to Phys. Rev. Let

Collisional Plasma Models with APEC/APED: Emission Line Diagnostics of Hydrogen-like and Helium-like Ions

New X-ray observatories (Chandra and XMM-Newton) are providing a wealth of high-resolution X-ray spectra in which hydrogen- and helium-like ions are usually strong features. We present results from a new collisional-radiative plasma code, the Astrophysical Plasma Emission Code (APEC), which uses atomic data in the companion Astrophysical Plasma Emission Database (APED) to calculate spectral models for hot plasmas. APED contains the requisite atomic data such as collisional and radiative rates, recombination cross sections, dielectronic recombination rates, and satellite line wavelengths. We compare the APEC results to other plasma codes for hydrogen- and helium-like diagnostics, and test the sensitivity of our results to the number of levels included in the models. We find that dielectronic recombination with hydrogen-like ions into high (n=6-10) principal quantum numbers affects some helium-like line ratios from low-lying (n=2) transitions.Comment: 5 pages, 6 figures, accepted by ApJ Letter

Phases of quantum states in completely positive non-unitary evolution

We define an operational notion of phases in interferometry for a quantum system undergoing a completely positive non-unitary evolution. This definition is based on the concepts of quantum measurement theory. The suitable generalization of the Pancharatnan connection allows us to determine the dynamical and geometrical parts of the total phase between two states linked by a completely positive map. These results reduce to the knonw expressions of total, dynamical and geometrical phases for pure and mixed states evolving unitarily.Comment: 2 figure

Mixed state geometric phases, entangled systems, and local unitary transformations

The geometric phase for a pure quantal state undergoing an arbitrary evolution is a ``memory'' of the geometry of the path in the projective Hilbert space of the system. We find that Uhlmann's geometric phase for a mixed quantal state undergoing unitary evolution not only depends on the geometry of the path of the system alone but also on a constrained bi-local unitary evolution of the purified entangled state. We analyze this in general, illustrate it for the qubit case, and propose an experiment to test this effect. We also show that the mixed state geometric phase proposed recently in the context of interferometry requires uni-local transformations and is therefore essentially a property of the system alone.Comment: minor changes, journal reference adde

Optical implementation and entanglement distribution in Gaussian valence bond states

We study Gaussian valence bond states of continuous variable systems, obtained as the outputs of projection operations from an ancillary space of M infinitely entangled bonds connecting neighboring sites, applied at each of $N$ sites of an harmonic chain. The entanglement distribution in Gaussian valence bond states can be controlled by varying the input amount of entanglement engineered in a (2M+1)-mode Gaussian state known as the building block, which is isomorphic to the projector applied at a given site. We show how this mechanism can be interpreted in terms of multiple entanglement swapping from the chain of ancillary bonds, through the building blocks. We provide optical schemes to produce bisymmetric three-mode Gaussian building blocks (which correspond to a single bond, M=1), and study the entanglement structure in the output Gaussian valence bond states. The usefulness of such states for quantum communication protocols with continuous variables, like telecloning and teleportation networks, is finally discussed.Comment: 15 pages, 6 figures. To appear in Optics and Spectroscopy, special issue for ICQO'2006 (Minsk). This preprint contains extra material with respect to the journal versio

Mutually unbiased bases: tomography of spin states and star-product scheme

Mutually unbiased bases (MUBs) are considered within the framework of a generic star-product scheme. We rederive that a full set of MUBs is adequate for a spin tomography, i.e. knowledge of all probabilities to find a system in each MUB-state is enough for a state reconstruction. Extending the ideas of the tomographic-probability representation and the star-product scheme to MUB-tomography, dequantizer and quantizer operators for MUB-symbols of spin states and operators are introduced, ordinary and dual star-product kernels are found. Since MUB-projectors are to obey specific rules of the star-product scheme, we reveal the Lie algebraic structure of MUB-projectors and derive new relations on triple- and four-products of MUB-projectors. Example of qubits is considered in detail. MUB-tomography by means of Stern-Gerlach apparatus is discussed.Comment: 11 pages, 1 table, partially presented at the 17th Central European Workshop on Quantum Optics (CEWQO'2010), June 6-11, 2010, St. Andrews, Scotland, U

Generalization of geometric phase to completely positive maps

We generalize the notion of relative phase to completely positive maps with known unitary representation, based on interferometry. Parallel transport conditions that define the geometric phase for such maps are introduced. The interference effect is embodied in a set of interference patterns defined by flipping the environment state in one of the two paths. We show for the qubit that this structure gives rise to interesting additional information about the geometry of the evolution defined by the CP map.Comment: Minor revision. 2 authors added. 4 pages, 2 figures, RevTex