Talks

The modern conception of phases of matter has undergone tremendous developments since the first observation of topologically ordered states in fractional quantum Hall systems in the 1980s. In this paper, we explore the question: In principle, how much detail of the physics of topological orders can be observed using state of the art technologies? We find that using surprisingly little data, namely the toric code Hamiltonian in the presence of generic disorders and detuning from its exactly solvable point, the modular matrices -- characterizing anyonic statistics that are some of the most fundamental fingerprints of topological orders -- can be reconstructed with very good accuracy solely by experimental means. This is a first experimental realization of these fundamental signatures of a topological order, a test of their robustness against perturbations, and a proof of principle -- that current technologies have attained the precision to identify phases of matter and, as such, probe an extended region of phase space around the soluble point before its breakdown. Given the special role of anyonic statistics in quantum computation, our work promises myriad applications in both probing and realistically harnessing these exotic phases of matter.

The distillation of quantum resources such as entanglement and coherence forms one of the most fundamental protocols in quantum information and is of outstanding operational significance, but it is often characterized in the idealized asymptotic limit where an unbounded number of independent and identically distributed copies of a quantum system are available. Physical considerations necessarily limit the number of copies available as well as restrict our ability to perform coherent state manipulations over a large numbers of systems, which makes it crucial to be able to characterize how well we can distill resources in realistic, non-asymptotic settings.

We introduce a framework for the non-asymptotic characterization of two related operational tasks, the distillation as well as environment-assisted distillation of quantum coherence. We establish a complete description of the achievable rates of distillation in the one-shot setting under several different classes of free operations, which we show to correspond to the optimization of smoothed entropic quantities as semidefinite programs. We introduce a class of coherence measures which quantify the best achievable fidelity of distillation, and use them to obtain an explicit analytical characterization of coherence distillation for all pure states. Further, we provide insight into the distillation of entanglement, revealing new operational similarities and differences between the resource theories of coherence and entanglement.

This talk is based on joint work with Kun Fang, Xin Wang, and Gerardo Adesso (arxiv:1711.10512) as well as with Ludovico Lami and Alexander Streltsov (in preparation).

Topological defect operators are extended operators in a quantum field theory (QFT) whose correlation functions are independent of continuous changes of the ambient space. They satisfy nontrivial fusion relations and put nontrivial constraints on the QFT itself and its deformations (such as renormalization group (RG) flows). Canonical examples of topological defect operators include generators of (higher-form) global symmetries whose constraints on the QFT have been well-studied. However they constitute just a tip of a much richer framework which we explore in detail in two spacetime dimensions. 

More specifically, we study the crossing relations of general topological defect lines (TDL) in two dimensions, discuss their relation to the usual 't Hooft anomalies associated to global symmetries, and use them to constrain RG flows to either conformal fixed points or topological quantum field theories (TQFTs). We show that if certain non-invertible TDLs are preserved along a RG flow, then the vacuum cannot be a non-degenerate gapped state. For various massive flows, we determine the infrared TQFTs completely from the consideration of TDLs together with modular invariance.

In 2020 the European Space Agency (ESA) will launch the Euclid satellite mission. Euclid is an ESA medium class astronomy and astrophysics space mission, and will undertake a galaxy redshift survey over the redshift range 0.9 < z < 1.8, while simultaneously performing an imaging survey in both visible and near infrared bands. The complete survey will provide hundreds of thousands images and several tens of Petabytes of data. About 10 billion sources will be observed by Euclid out of which several tens of million galaxy redshifts will be measured and used to make galaxy clustering measurements. These observations will be used to help to understand Dark Energy, the physical mechanism causing the current acceleration in the expansion of the Universe.

I will give a brief survey of the study of decomposable Specht modules for the symmetric group and its Hecke algebra, which includes results of Murphy, Dodge and Fayers, and myself. I will then report on an ongoing project with Louise Sutton, in which we are studying decomposable Specht modules for the Hecke algebra of type $B$ indexed by `bihooks’.