Efficient Characterisation and Optimal Control of Open Quantum Systems - Mathematical Foundations and Physical Applications

Since no physical system can ever be completely isolated from its environment, the study of open quantum systems is pivotal to reliably and accurately control complex quantum systems. In practice, reliability of the control field needs to be confirmed via certification of the target evolution while accuracy requires the derivation of high-fidelity control schemes in the presence of decoherence. In the first part of this thesis an algebraic framework is presented that allows to determine the minimal requirements on the unique characterisation of arbitrary unitary gates in open quantum systems, independent on the particular physical implementation of the employed quantum device. To this end, a set of theorems is devised that can be used to assess whether a given set of input states on a quantum channel is sufficient to judge whether a desired unitary gate is realised. This allows to determine the minimal input for such a task, which proves to be, quite remarkably, independent of system size. These results allow to elucidate the fundamental limits regarding certification and tomography of open quantum systems. The combination of these insights with state-of-the-art Monte Carlo process certification techniques permits a significant improvement of the scaling when certifying arbitrary unitary gates. This improvement is not only restricted to quantum information devices where the basic information carrier is the qubit but it also extends to systems where the fundamental informational entities can be of arbitary dimensionality, the so-called qudits. The second part of this thesis concerns the impact of these findings from the point of view of Optimal Control Theory (OCT). OCT for quantum systems utilises concepts from engineering such as feedback and optimisation to engineer constructive and destructive interferences in order to steer a physical process in a desired direction. It turns out that the aforementioned mathematical findings allow to deduce novel optimisation functionals that significantly reduce not only the required memory for numerical control algorithms but also the total CPU time required to obtain a certain fidelity for the optimised process. The thesis concludes by discussing two problems of fundamental interest in quantum information processing from the point of view of optimal control - the preparation of pure states and the implementation of unitary gates in open quantum systems. For both cases specific physical examples are considered: for the former the vibrational cooling of molecules via optical pumping and for the latter a superconducting phase qudit implementation. In particular, it is illustrated how features of the environment can be exploited to reach the desired targets.

Information processing by the school child : implications for teachers and counsellors.'Patrones del procesamiento de la información en la edad escolar : implicaciones para el profesorado y los orientadores'.

Resumen tomado de la publicación

Information processing: US Patent 4,409,617

An information processor for rendering input data compatible with standard video recording and/or display equipment, comprizing means for digitizing the input data over periods which are synchronous with the fields of a standard video signal, a store adapted to store the digitized data and release stored digitized data in correspondence wiht the line scan of a standard video monitor, the store having two halves which correspond to the interlaced fields of a standard video signal and being so arranged that one half is filed while the other is emptied, and means for converting the released stored digitized data into video luminance signals. The input signals may be in digital or analogue form. A second stage which reconstitutes the recorded data is also described.

Effects of active information processing on the understanding of risk information

Two experiments investigated effects of active processing of risk information on participants' understanding and judgments. It was hypothesized that more active processing would lead to better understanding and differences in affective judgments (e.g. increased satisfaction and reduced perceived risk to health). In both experiments participants were given a written scenario about their being prescribed a fictitious medication. This medication was said to cause side effects in 2% of people who took it. Before answering a series of written questions, participants in the active conditions of both experiments were asked to carry out a reflective task (portraying the size of risk on a bar chart in Experiment 1 and answering a reflective question in Experiment 2). The results showed that active participants rated the likelihood of experiencing possible side effects significantly lower than passive participants (Experiment 1), and that active participants were significantly more satisfied with the information and judged perceived risk to health from taking the medication significantly lower than passive participants (Experiment 2). In both experiments, active participants were significantly more correct in their probability and frequency estimates. The studies demonstrate that active processing of risk information leads to improved understanding of the information given. This has important implications for risk communication. In the context of health, better understanding should lead to improved decision-making and health outcomes. Copyright (C) 2004 John Wiley Sons, Ltd.

Intrusions in trauma and psychosis: information processing and phenomenology

Background: Intrusions are common symptoms of both posttraumatic stress disorder (PTSD) and schizophrenia. Steel et al (2005) suggest that an information processing style characterized by weak trait contextual integration renders psychotic individuals vulnerable to intrusive experiences. This ‘contextual integration hypothesis’ was tested in individuals reporting anomalous experiences in the absence of a need-for-care. Methods: Twenty-six low schizotypes and twenty-three individuals reporting anomalous experiences were shown a traumatic film with and without a concurrent visuo-spatial task. Participants rated post-traumatic intrusions for frequency and form, and completed self-report measures of information processing style. It was predicted that, due to their weaker trait contextual integration, the anomalous experiences group would (1) exhibit more intrusions following exposure to the trauma-film; (2) display intrusions characterised by more PTSD qualities and (3) show a greater reduction of intrusions with the concurrent visuo-spatial task. Results: As predicted, the anomalous experiences group reported a lower level of trait contextual integration and more intrusions than the low schizotypes, both immediately after watching the film, and during the following seven days. Their post-traumatic intrusive memories were more PTSD-like (more intrusive, vivid and associated with emotion). The visuo-spatial task had no effect on number of intrusions in either group. Conclusions: These findings provide some support for the proposal that weak trait contextual integration underlies the development of intrusions within both PTSD and psychosis.

A study of the relaxation dynamics in a quadrupolar NMR system using Quantum State Tomography

This article reports a relaxation study in an oriented system containing spin 3/2 nuclei using quantum state tomography (QST). The use of QST allowed evaluating the time evolution of all density matrix elements starting from several initial states. Using an appropriated treatment based on the Redfield theory, the relaxation rate of each density matrix element was measured and the reduced spectral densities that describe the system relaxation were determined. All the experimental data could be well described assuming pure quadrupolar relaxation and reduced spectral densities corresponding to a superposition of slow and fast motions. The data were also analyzed in the context of Quantum Information Processing, where the coherence loss of each qubit of the system was determined using the partial trace operation. (C) 2008 Elsevier Inc. All rights reserved.

Essays on decision sciences: exploring cognition, information processing, and complexity

This thesis provides three original contributions to the field of Decision Sciences. The first contribution explores the field of heuristics and biases. New variations of the Cognitive Reflection Test (CRT--a test to measure "the ability or disposition to resist reporting the response that first comes to mind"), are provided. The original CRT (S. Frederick [2005] Journal of Economic Perspectives, v. 19:4, pp.24-42) has items in which the response is immediate--and erroneous. It is shown that by merely varying the numerical parameters of the problems, large deviations in response are found. Not only the final results are affected by the proposed variations, but so is processing fluency. It seems that numbers' magnitudes serve as a cue to activate system-2 type reasoning. The second contribution explores Managerial Algorithmics Theory (M. Moldoveanu [2009] Strategic Management Journal, v. 30, pp. 737-763); an ambitious research program that states that managers display cognitive choices with a "preference towards solving problems of low computational complexity". An empirical test of this hypothesis is conducted, with results showing that this premise is not supported. A number of problems are designed with the intent of testing the predictions from managerial algorithmics against the predictions of cognitive psychology. The results demonstrate (once again) that framing effects profoundly affect choice, and (an original insight) that managers are unable to distinguish computational complexity problem classes. The third contribution explores a new approach to a computationally complex problem in marketing: the shelf space allocation problem (M-H Yang [2001] European Journal of Operational Research, v. 131, pp.107--118). A new representation for a genetic algorithm is developed, and computational experiments demonstrate its feasibility as a practical solution method. These studies lie at the interface of psychology and economics (with bounded rationality and the heuristics and biases programme), psychology, strategy, and computational complexity, and heuristics for computationally hard problems in management science.

Analysis of the chronic intake of and withdrawal from diazepam on emotional reactivity and sensory information processing in rats

It has been demonstrated that, on abrupt withdrawal, patients with chronic exposure can experience a number of symptoms indicative of a dependent state. In clinical patients, the earliest to arise and most persistent signal of withdrawal from chronic benzodiazepine (Bzp) treatment is anxiety. In laboratory animals, anxiety-like effects following abrupt interruption of chronic Bzp treatment can also be reproduced. In fact, signs that oscillate from irritability to extreme fear behaviours and seizures have been described already. As anxiety remains one of the most important symptoms of Bzp withdrawal, in this study we evaluated the anxiety levels of rats withdrawn from diazepam. Also studied were the effects on the motor performance and preattentive sensory gating process of rats under diazepam chronic treatment and upon 48-h withdrawal on three animal models of anxiety, the elevated plus-maze (EPM), ultrasonic vocalizations (USV) and startle + prepulse inhibition tests. Data obtained showed an anxiolytic- and anxiogenic-like profile of the chronic intake of and withdrawal from diazepam regimen in the EPM test, 22-KHz USV and startle reflex. Diazepam chronic effects or its withdrawal were ineffective in promoting any alteration in the prepulse inhibition (PPI). However, an increase of PPI was achieved in both sucrose and diazepam pretreated rats on 48-h withdrawal, suggesting a procedural rather than a specific effect of withdrawal on sensory gating processes. It is also possible that the prepulse can function as a conditioned stimulus to informing the delivery of an aversive event, as the auditory startling-eliciting stimulus. All these findings are indicative of a sensitization of the neural substrates of aversion in diazepam withdrawn animals without concomitant changes on the processing of sensory information

COMPLEXITY MEASURE: A QUANTUM INFORMATION APPROACH

In the past decades, all of the efforts at quantifying systems complexity with a general tool has usually relied on using Shannon's classical information framework to address the disorder of the system through the Boltzmann-Gibbs-Shannon entropy, or one of its extensions. However, in recent years, there were some attempts to tackle the quantification of algorithmic complexities in quantum systems based on the Kolmogorov algorithmic complexity, obtaining some discrepant results against the classical approach. Therefore, an approach to the complexity measure is proposed here, using the quantum information formalism, taking advantage of the generality of the classical-based complexities, and being capable of expressing these systems' complexity on other framework than its algorithmic counterparts. To do so, the Shiner-Davison-Landsberg (SDL) complexity framework is considered jointly with linear entropy for the density operators representing the analyzed systems formalism along with the tangle for the entanglement measure. The proposed measure is then applied in a family of maximally entangled mixed state.