This series consists of talks in the area of Foundations of Quantum Theory. Seminar and group meetings will alternate.
Quantum chaos is the study
of quantum systems whose classical description is chaotic.
In
a generic quantum experiment we have a given set of devices analyzing some
physical property of a system. To each device involved in the experiment we
associate a set of random outcomes corresponding to the possible values of the
variable analyzed by the device. Devices have apertures that permit physical
systems to pass through them. Each aperture is labelled as "input" or
"output" depending on whether it is assumed that the aperture lets
the system go inside or outside the device. Assuming a particular input/output
Negativity in a quasi-probability representation is typically
interpreted as an indication of nonclassical behavior.
However, this does not preclude bases that are non-negative from
having interesting applications---the single-qubit
stabilizer states have non-negative Wigner functions and yet
play a fundamental role in many quantum information tasks.
We determine what other sets of quantum states and measurements
of a qubit can be non-negative in a quasiprobability
If probabilities represent knowledge, what is an "unknown
probability"? De Finetti's theorem licenses the view that it is simply a
convenient metaphor for a certain class of knowledge about a series of
events. There are quantum versions for "unknown states" and
"unknown
channels". I will explain how "unknown measurements" can be
rehabilitated
too.
I will then move to a totally different topic. The Bloch sphere is handy
The fact that the quantum wavefunction of a many-particle system is a function on a high-dimensional configuration space, rather than on spacetime, has led some to suggest that any realist understanding of quantum mechanics must regard configuration space as more fundamental than spacetime. Worse, it seems that a wavefunction monist ontology cannot help itself to talk of "configuration space" at all, without particles for the configurations to be configurations of.
I will discuss the central role of correlations in
thermodynamic directionality, how strong correlations can distort the
thermodynamic arrow and contrast these distortions in both the classical and
quantum regimes. These distortions constitute non-linear entanglement witnesses,
and give rise to a rich information-theoretic structure. I shall explain how
these results are then cast into the language of fluctuation theorems to derive
a generalized exchange fluctuation theorem, and discuss the limitations of such
a framework.
I will
give an idea of what category theory is and how it can be successfully applied in mathematics and the mathematical sciences by means of example. The example is a notion from mathematical logic formalizing the intuitive concept of "property". The new category-theoretical
definition of this notion can physically be interpreted as a measurement. Unraveling this definition in particular categories can be regarded as defining the concept of "property" in different context, e.g. in classical, probabilistic
A very general way of describing the abstract structure of quantum theory is to say that the set of observables on a quantum system form a C*-algebra. A natural question is then, why should this be the case - why can observables be added and multiplied together to form any algebra, let alone of the special C* variety? I will present recent work with Markus Mueller and Howard Barnum, showing that the closest algebraic cousins to standard quantum theory, namely the Jordan-algebras, can be characterized by three principles having an informational ﬂavour, namely: (1) a generalized spectral d