I will discuss two
generalizations of Kochen-Specker (KS) sets: projective KS sets and generalized
KS sets. We will see that projective KS sets can be used to characterize all
graphs for which the chromatic number is strictly larger than the quantum
chromatic number. Here, the quantum chromatic number is defined via a nonlocal
game based on graph coloring. We will further show that from any graph with
separation between these two quantities, one can construct a classical channel
for which entanglement assistance increases the one-shot zero-error capacity.
As an example, we will consider a new family of classical channels with an
exponential increase.
We shall follow the
growth of probability theory and applications from the 1650s onwards, in
parallel with the development of statistical inference. Bayesian,
Neyman-Pearson hypothesis testing and Fisherian likelihood methods will all be
covered, with an emphasis on relating theory to a wide range of
applications. Practical sessions will use SciPy and feature
closed-form solutions, iterative and Monte Carlo simulation methods.
In this talk, I will present our recent work on the
effect of thermal fluctuations on the topological stability of chiral p-wave
superconductors. We consider two models of superconductors: spinless and
spinful with a focus on topological properties and Majorana zero-energy modes.
We show that proliferation of vortex-antivortex pairs above the
Kosterlitz-Thouless temperature T_KT drives the transition from a thermal Quantum
Hall insulator to a thermal metal/insulator, and dramatically modifies the
ground-state degeneracy splitting. This shows that in order to utilize 2D
chiral p-wave superconductors for topological quantum computing, the
temperature should be much smaller than T_KT.
Within the spinful chiral p-wave model, we also
investigate the interplay between half-quantum vortices carrying Majorana
zero-energy modes and full-quantum vortices having trivial topological charge,
and discuss topological properties of half-quantum vortices in the background
of proliferating full-quantum vortices.
We shall follow the
growth of probability theory and applications from the 1650s onwards, in
parallel with the development of statistical inference. Bayesian,
Neyman-Pearson hypothesis testing and Fisherian likelihood methods will all be
covered, with an emphasis on relating theory to a wide range of
applications. Practical sessions will use SciPy and feature
closed-form solutions, iterative and Monte Carlo simulation methods.
We shall follow the
growth of probability theory and applications from the 1650s onwards, in
parallel with the development of statistical inference. Bayesian,
Neyman-Pearson hypothesis testing and Fisherian likelihood methods will all be
covered, with an emphasis on relating theory to a wide range of
applications. Practical sessions will use SciPy and feature
closed-form solutions, iterative and Monte Carlo simulation methods.
Mark WiseCalifornia Institute of Technology (Caltech)
PIRSA:12090065
The crucial role that the Higgs boson plays in the
standard model for strong weak and electromagnetic interactions is reviewed.
Recently a resonance with properties consistent with
those expected for the Higgs boson has been discovered at the large hadron collider (LHC).
This discovery
constrains speculations about new physics beyond what is in the standard
model. The motivation for such new physics, at roughly the energy scale probed
by LHC experiments, and the nature of the constraints imposed by the recent
LHC results are discussed.