Scientific Series

How may we quantify the value of physical resources, such as entangled quantum states, heat baths or lasers? Existing resource theories give us partial answers; however, these rely on idealizations, like the concept of perfectly independent copies of states used to derive conversion rates. As these idealizations are impossible to implement in practice, such results may be of little consequence for experimentalists.

In this talk I introduce tools to quantify realistic descriptions of resources, applicable for example when we do not have perfect control over a physical system, when only the neighbourhood of a state or some of its properties are known, or when slight correlations cannot be ruled out.

Some resources, like entanglement, can be characterized in terms of copies of local states: we generalize this with operational ways to describe composition and copies of realistic resources, without assuming a tensor product structure.  For others, like thermodynamic work, value is seen as a real function on physical states, like the height of a weight. While value is often expected to behave linearly, that simplification excludes many real-life resources: for example, the operational value of money, in terms of what can be done with it, is hardly linear on the amount of coin, and even has catalytic aspects above certain thresholds. We characterize resources that behave linearly and those that allow for investments - in the extreme, catalytic resources.

This work is an application of the framework introduced in arXiv:1511.08818.

One implication of Bell's theorem is that there cannot in general be hidden variable models for quantum mechanics that both are noncontextual and retain the structure of a classical probability space.  Thus, some hidden variable programs aim to retain noncontextuality at the cost of using a generalization of the Kolmogorov probability axioms.  We present a theorem to show that such programs are committed to the existence of a finite null cover for some quantum mechanical experiments, i.e., a finite collection of probability zero events whose disjunction exhausts the space of possibilities.  This serves as a kind of "no-go" theorem for these alternative, or generalized, probability theories.

Categorical symplectic geometry studies an invariant of symplectic manifolds called the "Fukaya (A-infinity) category", which consists of the Lagrangian submanifolds and a symplectically-robust intersection theory of these Lagrangians.  Over the last two decades the Fukaya category has emerged as a powerful tool: for instance, it has produced inroads to Arnol'd's Nearby Lagrangians Conjecture, and it allowed Kontsevich to formulate the the Homological Mirror Symmetry conjecture.

In this talk I will describe a project, joint with Satyan Devadoss, Stefan Forcey, and Katrin Wehrheim, which attempts to relate the Fukaya categories of different symplectic manifolds via a notion of functoriality.  After mentioning some analytic results about the singular quilts necessary for this construction, I will describe the combinatorial component: with Devadoss and Forcey we are constructing a family of polytopes that specialize to the associahedra in two different ways, and can be thought of as the 2-categorical version of associahedra.

Generation of accurate mock observations tailored specifically to upcoming surveys such as Advanced ACT, CHIME, and LSST is a key technical challenge in cosmology. Traditional approaches involving N-body simulation are fraught with difficulties due to increasingly large survey volumes and depths. Typically, statistical ensembles can only be realized for a few carefully-chosen parameters, limiting exploration to a significantly restricted cosmological model space. We have developed a new massively parallel algorithm to generate accurate halo masses and positions in a fraction (~1e-3 to 1e-2) of the time taken by N-body simulations. I will present a suite of simulated full sky cluster Sunyaev-Zel’dovich maps that have been produced with this approach, and describe the types of virtual large scale structure observations that are now within reach in the coming years.

We study restrictions on locality-preserving unitary logical gates for topological quantum codes in two spatial dimensions.  A locality-preserving operation is one which maps local operators to local operators --- for example, a  constant-depth quantum circuit of geometrically local gates, or evolution for a constant time governed by a geometrically-local bounded-strength Hamiltonian. Locality-preserving logical gates of topological codes are intrinsically fault tolerant because spatially localized errors remain localized, and hence sufficiently dilute errors remain correctable. By invoking general properties of two-dimensional topological field theories, we find that the locality-preserving logical gates are severely limited for codes which admit non-abelian anyons; in particular, there are no locality-preserving logical gates on the torus or the sphere with M punctures if the braiding of anyons is computationally universal. Furthermore, for Ising anyons on the M-punctured sphere, locality-preserving gates must be elements of the logical Pauli group. We derive these results by relating logical gates of a topological code to automorphisms of the Verlinde algebra of the corresponding anyon model, and by requiring the logical gates to be compatible with basis changes in the logical Hilbert space arising from local F-moves and the mapping class group. 

This is joint work with Oliver Buerschaper, Robert Koenig, Fernando Pastawski and Sumit Sijher.

Time in quantum mechanics has duly received a lot of attention over the years. Perfect clocks which can turn on/off a particular interaction at a precise time that have been proposed only exist in infinite dimensions and have unphysical Hamiltonians (their spectrum is unbounded from below). It was this observation which led many to conclude that an operator for time cannot exist in quantum mechanics. Here, we prove rigorous results about the accuracy of finite dimensional clocks and show that they can well approximate their infinite dimensional counterparts under the right conditions.

Long-range quantum entanglement is now being recognized as a key characteristic of many novel states of quantum matter. The description of this entanglement requires the introduction of emergent “gauge fields”, much like those found in Maxwell’s theory of light. I will highlight some recent experiments on the copper-based high temperature superconductors, and interpret them using theories of emergent gauge fields.

The LHCb detector was designed to be the dedicated heavy-flavor physics experiment at the LHC, and has been the world's premier lab for studying processes where the net quark content changes for several years. These studies permit observing virtual contributions from beyond the SM particles up to very high mass scales, potentially (greatly) exceeding the direct reach of the LHC.  I will summarize the constraints placed on high-mass BSM physics by such studies, and also highlight a few interesting anomalies.  I will also discuss direct searches for low-mass BSM physics, and a selection of novel SM studies.  Finally, future prospects will be presented. 

One possibility for studying reheating is to link the duration and final temperature after reheating, and its equation of state, to inflationary observables. By restricting the equation of state to lie within a broad physically allowed range, one can bracket an allowed range of $n_s$ and $r$ for models of inflation. The results are similar to, but do a little better, than requiring the length of inflation lie between 50 and 60 efolds. The added constraints can help break degeneracies between inflation models that otherwise overlap in their predictions.

According to the standard model of cosmology 96% of the matter and energy in the universe is invisible. The dark matter particles comprising the invisible material have so far not been detected in laboratory and astrophysical experiments.  The dark energy responsible for the acceleration of the universe is still a controversial issue. A modified gravity theory is presented that can potentially fit current cosmological and astrophysical data. The black holes and their shadows predicted by MOG can differ from the predictions of Einstein gravity.

Fast radio bursts (FRBs) are bright, broadband, non-repeating, millisecond flashes of unknown astronomical origin. The dispersion of these bursts by intervening plasma suggests that the sources of the 16 bursts reported to date= are at 0.2<z<1. I will discuss the possibility of using dispersion, instead of redshift, to study the large-scale structure of the Universe in three dimensions. Like redshift, which is distorted by peculiar velocities, dispersion is an imperfect proxy for distance as it is distorted by inhomogeneities in the electron density. These dispersion-space distortions are calculable and actually greatly enhance the signal. The clustering signal in dispersion space could be detected in a survey of 10 000 FRBs, as is expected to be produced by the CHIME telescope over three years.

The greatest uncertainty in whether this technique will be successful is the unknown nature of FRB sources. A new observation tells us more about the environment of a source than ever before through the polarization and scattering properties of a burst. More observations of this type, along with observations that identify host galaxies, will soon tell whether FRBs will provide a new probe of structure.

Let $S$ be a surface, $G$ a semi-simple group of type B, C or D. I will explain why the moduli space of framed local systems $A_{G,S}$ defined by Fock and Goncharov has the structure of a cluster variety, and fits inside a larger structure called a cluster ensemble. This was previously known only in type A. This gives a more direct proof of results of Fock and Goncharov for the symplectic and spin groups, and also allows one to quantize higher Teichmuller space in these cases. If time permits, I hope to talk about applications to counting tensor invariants of finite dimensional representations of these groups.