On the nature and decay of quantum relative entropy

Historically at the core of thermodynamics and information theory, entropy's use in quantum information extends to diverse topics including high-energy physics and operator algebras. Entropy can gauge the extent to which a quantum system departs from classicality, including by measuring entanglement and coherence, and in the form of entropic uncertainty relations between incompatible measurements. The theme of this dissertation is the quantum nature of entropy, and how exposure to a noisy environment limits and degrades non-classical features. An especially useful and general form of entropy is the quantum relative entropy, of which special cases include the von Neumann and Shannon entropies, coherent and mutual information, and a broad range of resource-theoretic measures. We use mathematical results on relative entropy to connect and unify features that distinguish quantum from classical information. We present generalizations of the strong subadditivity inequality and uncertainty-like entropy inequalities to subalgebras of operators on quantum systems for which usual independence assumptions fail. We construct new measures of non-classicality that simultaneously quantify entanglement and uncertainty, leading to a new resource theory of operations under which these forms of non-classicalty become interchangeable. Physically, our results deepen our understanding of how quantum entanglement relates to quantum uncertainty. We show how properties of entanglement limit the advantages of quantum superadditivity for information transmission through channels with high but detectable loss. Our method, based on the monogamy and faithfulness of the squashed entanglement, suggests a broader paradigm for bounding non-classical effects in lossy processes. We also propose an experiment to demonstrate superadditivity. Finally, we estimate decay rates in the form of modified logarithmic Sobolev inequalities for a variety of quantum channels, and in many cases we obtain the stronger, tensor-stable form known as a complete logarithmic Sobolev inequality. We compare these with our earlier results that bound relative entropy of the outputs of a particular class of quantum channels

ON SYMMETRY: A FRAMEWORK FOR AUTOMATED SYMMETRY DETECTION

Symmetry has weaved itself into almost all fabrics of science, as well as in arts, and has left an indelible imprint on our everyday lives. And, in the same manner, it has pervaded a wide range of areas of computer science, especially computer vision area, and a copious amount of literature has been produced to seek an algorithmic way to identify symmetry in digital data. Notwithstanding decades of endeavor and attempt to have an efficient system that can locate and recover symmetry embedded in real-world images, it is still challenging to fully automate such tasks while maintaining a high level of efficiency. The subject of this thesis is symmetry of imaged objects. Symmetry is one of the non-accidental features of shapes and has long been (maybe mistakenly) speculated as a pre-attentive feature, which improves recognition of quickly presented objects and reconstruction of shapes from incomplete set of measurements. While symmetry is known to provide rich and useful geometric cues to computer vision, it has been barely used as a principal feature for applications because figuring out how to represent and recognize symmetries embedded in objects is a singularly difficult task, both for computer vision and for perceptual psychology. The three main problems addressed in the dissertation are: (i) finding approximate symmetry by identifying the most prominent axis of symmetry out of an entire region, (ii) locating bilaterally symmetrical areas from a scene, and (iii) automating the process of symmetry recovery by solving the problems mentioned above. Perfect symmetries are rare in the extreme in natural images and symmetry perception in humans allows for qualification so that symmetry can be graduated based on the degree of structural deformation or replacement error. There have been many approaches to detect approximate symmetry by searching an optimal solution in a form of an exhaustive exploration of the parameter space or surmising the center of mass. The algorithm set out in this thesis circumvents the computationally intensive operations by using geometric constraints of symmetric images, and assumes no prerequisite knowledge of the barycenter. The results from an extensive set of evaluation experiments on metrics for symmetry distance and a comparison of the performance between the method presented in this thesis and the state of the art approach are demonstrated as well. Many biological vision systems employ a special computational strategy to locate regions of interest based on local image cues while viewing a compound visual scene. The method taken in this thesis is a bottom-up approach that causes the observer favors stimuli based on their saliency, and creates a feature map contingent on symmetry. With the help of summed area tables, the time complexity of the proposed algorithm is linear in the size of the image. The distinguished regions are then delivered to the algorithm described above to uncover approximate symmetry

The electrophysiological response to visual symmetry: Hemisphere lateralisation and visual clutter

The experiments reported in this thesis explore the electrophysiological response to visual symmetry. Symmetry is an important visual feature in object recognition and image segmentation that is efficiently processed by the visual system. Neuroimaging and electrophysiological research has provided a greater understanding of how the human brain processes symmetry. ERP research has identified a neural signature for symmetry processing termed the Sustained Posterior Negativity (SPN): Lower amplitude is observed in posterior electrodes for symmetrical than random patterns from around 200ms after stimulus onset. This thesis will address four important and novel questions: (1) Can the SPN be produced independently within each hemisphere? (2) Is right lateralised alpha desynchronisation during regularity discrimination the result of hemisphere specialisation or directed spatial attention? (3) Does visual crowding influence the SPN? and (4) How does figure-ground assignment influence the neural response to symmetry? The current studies show for the first time that the SPN can be produced to stimuli in the periphery with symmetry processed by independent symmetry sensitive networks within each hemisphere. It also offers evidence that the right hemisphere may be specialised for symmetry perception. Moreover, figure-ground assignment and visual crowding are shown to modulate the SPN. Together these experiments highlight that this automatic response to symmetry is processed independently in each hemisphere and is subject to bottom-up stimulus characteristics