2,667 research outputs found
Categorical Quantum Dynamics
We use strong complementarity to introduce dynamics and symmetries within the
framework of CQM, which we also extend to infinite-dimensional separable
Hilbert spaces: these were long-missing features, which open the way to a
wealth of new applications. The coherent treatment presented in this work also
provides a variety of novel insights into the dynamics and symmetries of
quantum systems: examples include the extremely simple characterisation of
symmetry-observable duality, the connection of strong complementarity with the
Weyl Canonical Commutation Relations, the generalisations of Feynman's clock
construction, the existence of time observables and the emergence of quantum
clocks.
Furthermore, we show that strong complementarity is a key resource for
quantum algorithms and protocols. We provide the first fully diagrammatic,
theory-independent proof of correctness for the quantum algorithm solving the
Hidden Subgroup Problem, and show that strong complementarity is the feature
providing the quantum advantage. In quantum foundations, we use strong
complementarity to derive the exact conditions relating non-locality to the
structure of phase groups, within the context of Mermin-type non-locality
arguments. Our non-locality results find further application to quantum
cryptography, where we use them to define a quantum-classical secret sharing
scheme with provable device-independent security guarantees.
All in all, we argue that strong complementarity is a truly powerful and
versatile building block for quantum theory and its applications, and one that
should draw a lot more attention in the future.Comment: Thesis submitted for the degree of Doctor of Philosophy, Oxford
University, Michaelmas Term 2016 (273 pages
The development of a temporal-BRDF model-based approach to change detection, an application to the identification and delineation of fire affected areas.
Although large quantities of southern Africa burn every year, minimal information is available relating to the fire regimes of this area. This study develops a new, generic approach to change detection, applicable to the identification of land cover change from high temporal and moderate spatial resolution satellite data. Traditional change detection techniques have several key limitations which are identified and addressed in this work. In particular these approaches fail to account for directional effects in the remote sensing signal introduced by variations in the solar and sensing geometry, and are sensitive to underlying phenological changes in the surface as well as noise in the data due to cloud or atmospheric contamination. This research develops a bi-directional, model-based change detection algorithm. An empirical temporal component is incorporated into a semi-empirical linear BRDF model. This may be fitted to a long time series of reflectance with less sensitivity to the presence of underlying phenological change. Outliers are identified based on an estimation of noise in the data and the calculation of uncertainty in the model parameters and are removed from the sequence. A "step function kernel" is incorporated into the formulation in order to detect explicitly sudden step-like changes in the surface reflectance induced by burning. The change detection model is applied to the problem of locating and mapping fire affected areas from daily moderate spatial resolution satellite data, and an indicator of burn severity is introduced. Monthly burned area datasets for a 2400km by 1200km area of southern Africa detailing the day and severity of burning are created for a five year period (2000-2004). These data are analysed and the fire regimes of southern African ecosystems during this time are characterised. The results highlight the extent of the burning which is taking place within southern Africa, with between 27-32% of the study area burning during each of the five years of observation. Higher fire frequencies are exhibited by savanna and grassland ecosystems, while more dense vegetation types such as shrublands and deciduous broadleaf forests burn less frequently. In addition the areas which burn more frequently do so with a greater severity, with a positive relationship identified between the frequency and the severity of burning
Do We Understand Quantum Mechanics - Finally?
After some historical remarks concerning Schroedinger's discovery of wave
mechanics, we present a unified formalism for the mathematical description of
classical and quantum-mechanical systems, utilizing elements of the theory of
operator algebras. We then review some basic aspects of quantum mechanics and,
in particular, of its interpretation. We attempt to clarify what Quantum
Mechanics tells us about Nature when appropriate experiments are made. We
discuss the importance of the mechanisms of "dephasing" and "decoherence" in
associating "facts" with possible events and rendering complementary possible
events mutually exclusive.Comment: 42 pages, contribution to the Proceedings of a conference in memory
of Erwin Schroedinger, Vienna, January 201
Entanglement and separability of quantum harmonic oscillator systems at finite temperature
In the present paper we study the entanglement properties of thermal (a.k.a.
Gibbs) states of quantum harmonic oscillator systems as functions of the
Hamiltonian and the temperature. We prove the physical intuition that at
sufficiently high temperatures the thermal state becomes fully separable and we
deduce bounds on the critical temperature at which this happens. We show that
the bound becomes tight for a wide class of Hamiltonians with sufficient
translation symmetry. We find, that at the crossover the thermal energy is of
the order of the energy of the strongest normal mode of the system and quantify
the degree of entanglement below the critical temperature. Finally, we discuss
the example of a ring topology in detail and compare our results with previous
work in an entanglement-phase diagram.Comment: 10 pages, 5 figure
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