Quantum Foundations

This series consists of talks in the area of Foundations of Quantum Theory. Seminar and group meetings will alternate.

Seminar Series Events/Videos

Currently there are no upcoming talks in this series.

 

Tuesday Nov 20, 2007
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Several finite dimensional quasi-probability representations of quantum states have been proposed to study various problems in quantum information theory and quantum foundations. These representations are often defined only on restricted dimensions and their physical significance in contexts such as drawing quantum-classical comparisons is limited by the non-uniqueness of the particular representation.

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Tuesday Nov 13, 2007
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A new microcanonical equilibrium state is introduced for quantum systems with finite-dimensional state spaces. Equilibrium is characterised by a uniform distribution on a level surface of the expectation value of the Hamiltonian. The distinguishing feature of the proposed equilibrium state is that the corresponding density of states is a continuous function of the energy, and hence thermodynamic functions are well defined for finite quantum systems. The density of states, however, is not in general an analytic function.

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Thursday Nov 08, 2007
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What if the second law of thermodynamics, in the hierarchy of physical laws, were at the same level as the fundamental laws of mechanics, such as the great conservation principles? What if entropy were an intrinsic property of matter at the same level as energy is universally understood to be? What if irreversibility were an intrinsic feature of the microscopic dynamical law of all physical objects, including an individual qubit or qudit?

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Tuesday Oct 30, 2007
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The simplest algebraic curves of genus one are the nonsingular cubics in two-dimensional complex projective space. Interpreting CP^2 as the space of pure quantum states associated with a Hilbert space of dimension three, I will show how various properties of d=3 symmetric informationally complete positive operator valued measures can be understood in terms of the geometry of such curves. The resulting structure, although of considerable complexity, is very beautiful from a mathematical perspective.

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Tuesday Oct 23, 2007
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The solution of many problems in quantum information is critically dependent on the geometry of the space of density matrices. For a Hilbert space of dimension 2 this geometry is very simple: it is simply a sphere. However for Hilbert spaces of dimension greater than 2 the geometry is much more interesting as the bounding hypersurface is both highly symmetric (it has a d^2 real parameter symmetry group, where d is the dimension) and highly convoluted. The problem of getting a better understanding of this hypersurface is difficult (it is hard even in the case of a single qutrit).

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Thursday Mar 15, 2007
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Results in decoherence theory and entanglement theory will be considered as tools illuminating the foundation of quantum mechanics and the possible relationship of quantum information to it.

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Monday Jan 22, 2007
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The mathematical formalism of quantum theory has many features whose physical origin remains obscure. In this paper, we attempt to systematically investigate the possibility that the concept of information may play a key role in understanding some of these features. We formulate a set of assumptions, based on generalizations of experimental facts that are representative of quantum phenomena and physically comprehensible theoretical ideas and principles, and show that it is possible to deduce the finite-dimensional quantum formalism from these assumptions.

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Monday Feb 20, 2006

Collapse models are one of the most promising attempts to overcome the measurement problem of quanum mechanics: they descibe, within one single framework, both the quantum properties of microscopic systems and the classical properties of macroscopic objects, and in particular they explain why measurements always have definite outcomes, distributed according to the Born probability rule.

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