Classical vs. Quantum Decoherence

Based on the superposition principle, any two states of a quantum system may be coherently superposed to yield a novel state. Such a simple construction is at the heart of genuinely quantum phenomena such as interference of massive particles or quantum entanglement. Yet, these superpositions are susceptible to environmental influences, eventually leading to a complete disappearance of the system's quantum character. In principle, two distinct mechanisms responsible for this process of decoherence may be identified. In a classical decoherence setting, on the one hand, stochastic fluctuations of classical, ambient fields are the relevant source. This approach leads to a formulation in terms of stochastic Hamiltonians; the dynamics is unitary, yet stochastic. In a quantum decoherence scenario, on the other hand, the system is described in the language of open quantum systems. Here, the environmental degrees of freedom are to be treated quantum mechanically, too. The loss of coherence is then a direct consequence of growing correlations between system and environment. The purpose of the present thesis is to clarify the distinction between classical and quantum decoherence. It is known that there exist decoherence processes that are not reconcilable with the classical approach. We deem it desirable to have a simple, feasible model at hand of which it is known that it cannot be understood in terms of fluctuating fields. Indeed, we find such an example of true quantum decoherence. The calculation of the norm distance to the convex set of classical dynamics allows for a quantitative assessment of the results. In order to incorporate genuine irreversibility, we extend the original toy model by an additional bath. Here, the fragility of the true quantum nature of the dynamics under increasing coupling strength is evident. The geometric character of our findings offers remarkable insights into the geometry of the set of non-classical decoherence maps. We give a very intuitive geometrical measure---a volume---for the quantumness of dynamics. This enables us to identify the decoherence process of maximum quantumness, that is, having maximal distance to the convex set of dynamics consistent with the stochastic, classical approach. In addition, we observe a distinct correlation between the decoherence potential of a given dynamics and its achievable quantumness. In a last step, we study the notion of quantum decoherence in the context of a bipartite system which couples locally to the subsystems' respective environments. A simple argument shows that in the case of a separable environment the resulting dynamics is of classical nature. Based on a realistic experiment, we analyze the impact of entanglement between the local environments on the nature of the dynamics. Interestingly, despite the variety of entangled environmental states scrutinized, no single instance of true quantum decoherence is encountered. In part, the identification of the classical nature relies on numerical schemes. However, for a large class of dynamics, we are able to exclude analytically the true quantum nature

Decoherence and Entanglement Dynamics in Fluctuating Fields

We study pure phase damping of two qubits due to fluctuating fields. As frequently employed, decoherence is thus described in terms of random unitary (RU) dynamics, i.e., a convex mixture of unitary transformations. Based on a separation of the dynamics into an average Hamiltonian and a noise channel, we are able to analytically determine the evolution of both entanglement and purity. This enables us to characterize the dynamics in a concurrence-purity (CP) diagram: we find that RU phase damping dynamics sets constraints on accessible regions in the CP plane. We show that initial state and dynamics contribute to final entanglement independently.Comment: 10 pages, 5 figures, added minor changes in order to match published versio

Quantum Decoherence of Two Qubits

It is commonly stated that decoherence in open quantum systems is due to growing entanglement with an environment. In practice, however, surprisingly often decoherence may equally well be described by random unitary dynamics without invoking a quantum environment at all. For a single qubit, for instance, pure decoherence (or phase damping) is always of random unitary type. Here, we construct a simple example of true quantum decoherence of two qubits: we present a feasible phase damping channel of which we show that it cannot be understood in terms of random unitary dynamics. We give a very intuitive geometrical measure for the positive distance of our channel to the convex set of random unitary channels and find remarkable agreement with the so-called Birkhoff defect based on the norm of complete boundedness.Comment: 5 pages, 4 figure

A Novel Approach for Modeling Neural Responses to Joint Perturbations Using the NARMAX Method and a Hierarchical Neural Network

The human nervous system is an ensemble of connected neuronal networks. Modeling and system identification of the human nervous system helps us understand how the brain processes sensory input and controls responses at the systems level. This study aims to propose an advanced approach based on a hierarchical neural network and non-linear system identification method to model neural activity in the nervous system in response to an external somatosensory input. The proposed approach incorporates basic concepts of Non-linear AutoRegressive Moving Average Model with eXogenous input (NARMAX) and neural network to acknowledge non-linear closed-loop neural interactions. Different from the commonly used polynomial NARMAX method, the proposed approach replaced the polynomial non-linear terms with a hierarchical neural network. The hierarchical neural network is built based on known neuroanatomical connections and corresponding transmission delays in neural pathways. The proposed method is applied to an experimental dataset, where cortical activities from ten young able-bodied individuals are extracted from electroencephalographic signals while applying mechanical perturbations to their wrist joint. The results yielded by the proposed method were compared with those obtained by the polynomial NARMAX and Volterra methods, evaluated by the variance accounted for (VAF). Both the proposed and polynomial NARMAX methods yielded much better modeling results than the Volterra model. Furthermore, the proposed method modeled cortical responded with a mean VAF of 69.35% for a three-step ahead prediction, which is significantly better than the VAF from a polynomial NARMAX model (mean VAF 47.09%). This study provides a novel approach for precise modeling of cortical responses to sensory input. The results indicate that the incorporation of knowledge of neuroanatomical connections in building a realistic model greatly improves the performance of system identification of the human nervous system

Environment-Assisted Error Correction of Single-Qubit Phase Damping

Open quantum system dynamics of random unitary type may in principle be fully undone. Closely following the scheme of environment-assisted error correction proposed by Gregoratti and Werner [M. Gregoratti and R. F. Werner, J. Mod. Opt. 50(6), 915-933 (2003)], we explicitly carry out all steps needed to invert a phase-damping error on a single qubit. Furthermore, we extend the scheme to a mixed-state environment. Surprisingly, we find cases for which the uncorrected state is closer to the desired state than any of the corrected ones

Abschlussbericht zum Verbundprojekt InKola: Infrastrukturkopplung - Platzierung und Betrieb von Ladestationen aus Verkehrs- und Energienetzsicht

Im Mittelpunkt des Vorhabens InKola „Infrastrukturkopplung – Platzierung und Betrieb von Ladestationen aus Verkehrs- und Energienetzsicht“ steht die infrastrukturübergreifende Planung und der Betrieb für Verkehr- und Energiesysteme. Das Ziel ist es, zusammen der Stadt Burg ein anwendungsorientiertes Konzept zur optimalen Platzierung, Versorgung und Betrieb von Ladeinfrastruktur aus Netz- und Verkehrssicht unter Einbindung erneuerbarer Erzeugung zu entwickeln, und an ausgewählten Standorten in der Stadt Burg Ladeinfrastruktur zu installieren

Dynamic Information Flow Based on EEG and Diffusion MRI in Stroke: A Proof-of-Principle Study

In hemiparetic stroke, functional recovery of paretic limb may occur with the reorganization of neural networks in the brain. Neuroimaging techniques, such as magnetic resonance imaging (MRI), have a high spatial resolution which can be used to reveal anatomical changes in the brain following a stroke. However, low temporal resolution of MRI provides less insight of dynamic changes of brain activity. In contrast, electro-neurophysiological techniques, such as electroencephalography (EEG), have an excellent temporal resolution to measure such transient events, however are hindered by its low spatial resolution. This proof-of-principle study assessed a novel multimodal brain imaging technique namely Variational Bayesian Multimodal Encephalography (VBMEG), which aims to improve the spatial resolution of EEG for tracking the information flow inside the brain and its changes following a stroke. The limitations of EEG are complemented by constraints derived from anatomical MRI and diffusion weighted imaging (DWI). EEG data were acquired from individuals suffering from a stroke as well as able-bodied participants while electrical stimuli were delivered sequentially at their index finger in the left and right hand, respectively. The locations of active sources related to this stimulus were precisely identified, resulting in high Variance Accounted For (VAF above 80%). An accurate estimation of dynamic information flow between sources was achieved in this study, showing a high VAF (above 90%) in the cross-validation test. The estimated dynamic information flow was compared between chronic hemiparetic stroke and able-bodied individuals. The results demonstrate the feasibility of VBMEG method in revealing the changes of information flow in the brain after stroke. This study verified the VBMEG method as an advanced computational approach to track the dynamic information flow in the brain following a stroke. This may lead to the development of a quantitative tool for monitoring functional changes of the cortical neural networks after a unilateral brain injury and therefore facilitate the research into, and the practice of stroke rehabilitation

A rigorous model of reflex function indicates that position and force feedback are flexibly tuned to position and force tasks

This study aims to quantify the separate contributions of muscle force feedback, muscle spindle activity and co-contraction to the performance of voluntary tasks (“reduce the influence of perturbations on maintained force or position”). Most human motion control studies either isolate only one contributor, or assume that relevant reflexive feedback pathways during voluntary disturbance rejection tasks originate mainly from the muscle spindle. Human ankle-control experiments were performed, using three task instructions and three perturbation characteristics to evoke a wide range of responses to force perturbations. During position tasks, subjects (n = 10) resisted the perturbations, becoming more stiff than when being relaxed (i.e., the relax task). During force tasks, subjects were instructed to minimize force changes and actively gave way to imposed forces, thus becoming more compliant than during relax tasks. Subsequently, linear physiological models were fitted to the experimental data. Inhibitory, as well as excitatory force feedback, was needed to account for the full range of measured experimental behaviors. In conclusion, force feedback plays an important role in the studied motion control tasks (excitatory during position tasks and inhibitory during force tasks), implying that spindle-mediated feedback is not the only significant adaptive system that contributes to the maintenance of posture or force

Getting Down to Specifics: Profiling Gene Expression and Protein-DNA Interactions in a Cell Type-Specific Manner.

The majority of multicellular organisms are comprised of an extraordinary range of cell types, with different properties and gene expression profiles. Understanding what makes each cell type unique, and how their individual characteristics are attributed, are key questions for both developmental and neurobiologists alike. The brain is an excellent example of the cellular diversity expressed in the majority of eukaryotes. The mouse brain comprises of approximately 75 million neurons varying in morphology, electrophysiology, and preferences for synaptic partners. A powerful process in beginning to pick apart the mechanisms that specify individual characteristics of the cell, as well as their fate, is to profile gene expression patterns, chromatin states, and transcriptional networks in a cell type-specific manner, i.e. only profiling the cells of interest in a particular tissue. Depending on the organism, the questions being investigated, and the material available, certain cell type-specific profiling methods are more suitable than others. This chapter reviews the approaches presently available for selecting and isolating specific cell types and evaluates their key features