This series consists of talks in the area of Foundations of Quantum Theory. Seminar and group meetings will alternate.
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 de
It is certainly possible to express ordinary quantum mechanics in the framework of a real vector space: by adopting a suitable restriction on all operators--Stueckelberg’s rule--one can make the real-vector-space theory exactly equivalent to the standard complex theory. But can we achieve a similar effect without invoking such a restriction? In this talk I explore a model within real-vector-space quantum theory in which the role of the complex phase is played by a separate physical system called the ubit (for “universal rebit”). The ubit is a single binary real-vector-space quantum objec
The distinction between a realist interpretation of quantum theory that is psi-ontic and one that is psi-epistemic is whether or not a difference in the quantum state necessarily implies a difference in the underlying ontic state. Psi-ontologists believe that it does, psi-epistemicists that it does not. This talk will address the question of whether the PBR theorem should be interpreted as lending evidence against the psi-epistemic research program.