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
representation, and identify nontrivial groups of unitary
transformations that permute such states. These sets of states
and measurements are analogous to the single-qubit stabilizer
states. We show that no quasiprobability representation of a
qubit can be non-negative for more than two bases in any plane
of the Bloch sphere. Furthermore, there is a single family of
sets of four bases that can be non-negative in an arbitrary
quasiprobability representation of a qubit. We provide an
exhaustive list of the sets of single-qubit bases that are nonnegative
in some quasiprobability representation and are also
closed under a group of unitary transformations, revealing two
families of such sets of three bases. We also show that not
all two-qubit Clifford transformations can preserve
non-negativity in any quasiprobability representation that is
non-negative for the computational basis. This is in stark
contrast to the qutrit case, in which the discrete Wigner
function is non-negative for all n-qutrit stabilizer states and
Clifford transformations. We also provide some evidence
that extending the other sets of non-negative single-qubit
states to multiple qubits does not give entangled states.
I will discuss recent progress in the study of
anomaly-induced transport, focusing on the chiral vortical effect in 3+1 dimensions.
Most of my discussion will be framed in light of a larger story, namely
progress in making exact statements about finite-temperature quantum field
theory, for which the chiral magnetic and vortical effects are instructive
prototypes.
Light third generation
superpartners are one way to avoid bounds on new physics from the early
LHC. We will review the theory and phenomenology of light stops and highlight a
particular UV model based a partially composite electroweak sector through
Seiberg duality.
The de Sitter S-matrix provides a gauge-invariant and
field redefinition-invariant window into de Sitter QFTs and may provide a
crucial entry in any dS/CFT dictionary. In this talk I will summarize recent
progress on developing the S-matrix for theories with gauge fields and
perturbative gravity. Nonrenormalization theorems, hints of supersymmetry, and
perturbative stability will be discussed.
Using techniques originating in a certain
approach to Clifford bundles known as "geometric algebra", I discuss
a geometric reformulation of constrained generalized Killing spinor equations
which proves to be particularly effective in the study and classification of
supersymmetric flux compactifications of string and M-theory. As an
application, I discuss the most general N=2 compactifications of M-theory to
three dimensions, which were never studied in full generality before. I also
touch upon the connection of such techniques with a certain variant of the
quantization of spin systems.
We describe of the evaporation
process as driven by the dynamical evolution of the quantum gravitational
degrees of freedom resident at the horizon, as identified by the Loop Quantum
Gravity kinematics. Using a parallel with the Brownian motion, we interpret the
first law of quantum dynamical horizon in terms of a fluctuation-dissipation
relation applied to this fundamental discrete structure. In this way, the
horizon evolution is described in terms of relaxation to an equilibrium state
balanced by the excitation of Planck scale constituents of the horizon. We show
how from this setting the emergence of several conservative scenarios for the
final stage of the evaporation process can be microscopically derived. Namely,
the leakage of part of the horizon quantum geometry information prior to the
Planckian phase and the stabilization of the hole surface shrinkage forming a
massive remnant, which can eventually decay, are shown to take place.