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

Geometric Quantum Computation

We describe in detail a general strategy for implementing a conditional geometric phase between two spins. Combined with single-spin operations, this simple operation is a universal gate for quantum computation, in that any unitary transformation can be implemented with arbitrary precision using only single-spin operations and conditional phase shifts. Thus quantum geometrical phases can form the basis of any quantum computation. Moreover, as the induced conditional phase depends only on the geometry of the paths executed by the spins it is resilient to certain types of errors and offers the potential of a naturally fault-tolerant way of performing quantum computation.Comment: 15 pages, LaTeX, uses cite, eepic, epsfig, graphicx and amsfonts. Accepted by J. Mod. Op

Instructional Design for Advanced Learners: Establishing Connections between the Theoretical Frameworks of Cognitive Load and Deliberate Practice

Cognitive load theory (CLT) has been successful in identifying instructional formats that are more effective and efficient than conventional problem solving in the initial, novice phase of skill acquisition. However, recent findings regarding the “expertise reversal effect” have begun to stimulate cognitive load theorists to broaden their horizon to the question of how instructional design should be altered as a learner's knowledge increases. To answer this question, it is important to understand how expertise is acquired and what fosters its development. Expert performance research, and, in particular, the theoretical framework of deliberate practice have given us a better understanding of the principles and activities that are essential in order to excel in a domain. This article explores how these activities and principles can be used to design instructional formats based on CLT for higher levels of skills mastery. The value of these formats for e-learning environments in which learning tasks can be adaptively selected on the basis of online assessments of the learner's level of expertise is discussed

Geometric Phases for Mixed States during Cyclic Evolutions

The geometric phases of cyclic evolutions for mixed states are discussed in the framework of unitary evolution. A canonical one-form is defined whose line integral gives the geometric phase which is gauge invariant. It reduces to the Aharonov and Anandan phase in the pure state case. Our definition is consistent with the phase shift in the proposed experiment [Phys. Rev. Lett. \textbf{85}, 2845 (2000)] for a cyclic evolution if the unitary transformation satisfies the parallel transport condition. A comprehensive geometric interpretation is also given. It shows that the geometric phases for mixed states share the same geometric sense with the pure states.Comment: 9 pages, 1 figur

Expertise Shapes Multimodal Imagery for Wine

Although taste and smell seem hard to imagine, some people nevertheless report vivid imagery in these sensory modalities. We investigate whether experts are better able to imagine smells and tastes because they have learned the ability, or whether they are better imaginers in the first place, and so become experts. To test this, we first compared a group of wine experts to yoked novices using a battery of questionnaires. We show for the first time that experts report greater vividness of wine imagery, with no difference in vividness across sensory modalities. In contrast, novices had more vivid color imagery than taste or odor imagery for wines. Experts and novices did not differ on other vividness of imagery measures, suggesting a domain-specific effect of expertise. Critically, in a second study, we followed a group of students commencing a wine course and a group of matched control participants. Students and controls did not differ before the course, but after the wine course students reported more vivid wine imagery. We provide evidence that expertise improves imagery, exemplifying the extent of plasticity of cognition underlying the chemical senses

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

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

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