This series consists of talks in the area of Foundations of Quantum Theory. Seminar and group meetings will alternate.
A quantum steering ellipsoid may be used to faithfully represent
a density matrix ? describing two qubits A and B. The ellipsoid is the
geometric set of states that Bob can steer Alice's qubit to when he implements
all possible measurements on his qubit. We show how the correlations between
qubits A and B manifest themselves in this paradigm, giving simple conditions
for when the state is entangled, or has discord. We will also present novel features
of the two qubit state that are revealed by the steering ellipsoid formalism,
Crudely formulated, the idea of neorealism, in the way that
Chris Isham and Andreas Doering use it, means that each theory of
physics, in its mathematical formulation should share certain structural
properties of classical physics. These properties are chosen to allow some degree of
realism in the interpretation (for example, physical variables always have values).
Apart from restricting the form of physical theories, neorealism does
increase freedom in the shape of physical theories in another
The general boundary formulation (GBF) is an atemporal, but spacetime local formulation of quantum theory. Usually it is presented in terms of the amplitude formalism, which, in the presence of a background time, recovers the pure state formalism of the standard formulation of quantum theory. After reviewing the essentials of the amplitude formalism I will introduce a new "positive formalism", which recovers instead a mixed state formalism.
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