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The predictions of quantum theory resist generalised noncontextual explanations. In addition to the foundational relevance of this fact, the particular extent to which quantum theory violates noncontextuality limits available quantum advantage in communication and information processing. In the first part of this work, we formally define contextuality scenarios via prepare-and-measure experiments, along with the polytope of general contextual behaviours containing the set of quantum contextual behaviours. This framework allows us to recover several properties of set of quantum behaviours in these scenarios . Most surprisingly, we discover contextuality scenarios and associated noncontextuality inequalities that require for their violation the individual quantum preparation and measurement procedures to be mixed states and unsharp measurements. With the framework in place, we formulate novel semidefinite programming relaxations for bounding these sets of quantum contextual behaviours. Most significantly, to circumvent the inadequacy of pure states and projective measurements in contextuality scenarios, we present a novel unitary operator based semidefinite relaxation technique. We demonstrate the efficacy of these relaxations by obtaining tight upper bounds on the quantum violation of several noncontextuality inequalities and identifying novel maximally contextual quantum strategies. To further illustrate the versatility of these relaxations we demonstrate the monogamy of preparation contextuality in a tripartite setting, and present a secure semi-device independent quantum key distribution scheme powered by quantum advantage in parity oblivious random access codes.

In the last two decades the field of nonequilibrium quantum many-body physics
has seen a rapid development driven, in particular, by the remarkable progress
in quantum simulators, which today provide access to dynamics in quantum
matter with an unprecedented control. However, the efficient numerical
simulation of nonequilibrium real-time evolution in isolated quantum matter
still remains a key challenge for current computational methods especially
beyond one spatial dimension. In this talk I will present a versatile and
efficient machine learning inspired approach. I will first introduce the
general idea of encoding quantum many-body wave functions into artificial
neural networks. I will then identify and resolve key challenges for the
simulation of real-time evolution, which previously imposed significant
limitations on the accurate description of large systems and long-time
dynamics. As a concrete example, I will consider the dynamics of the
paradigmatic two-dimensional transverse field Ising model, where we observe
collapse and revival oscillations of ferromagnetic order and demonstrate that
the reached time scales are comparable to or exceed the capabilities of state-
of-the-art tensor network methods.

I describe the non-relativistic c→∞ and ultra-relativistic c→0 limits of the kappa-deformed symmetries, with and without a cosmological constant.  The corresponding kappa-Newtonian and kappa-Carrollian noncommutative spacetimes are also obtained. These constructions show the non-trivial interplay between the quantum deformation parameter kappa, the curvature parameter Lambda and the speed of light parameter c.

Human contact patterns are highly heterogeneous in terms of the both the number and nature of interactions. To incorporate these heterogeneities into infectious disease models one naturally represents a population as a weighted network. While there is a large literature on the spread of diseases on networks, most techniques are highly computational in nature. In this talk I will talk about an analytical framework for modeling infectious diseases as a percolation process on weighted networks based on probability generating functions. 

In the context of vaccination, human contact heterogeneities become a resource: Vaccinating individuals with greater total exposure leads to a greater reduction in disease spread. We have proposed that exposure notification apps, such as COVID Alert, can be leveraged to improve vaccine uptake among high exposure individuals, thereby optimizing our limited COVID-19 vaccine supply. We demonstrate the efficiency of this proposal using our weighted percolation theory framework.

Motivated by Feynman's early proposal, several schemes have been proposed recently to explore the quantum nature of gravity using table-top experiments. The key idea behind them is to study whether gravity can lead to non-classical quantum correlations between two objects. These experiments, if successful, can test different models of quantum gravity in the Newtonian limit. In this talk, I will discuss one such scheme based upon optomechanics that couples light to mechanical oscillators mediated by quantum radiation pressure. The non-classicality of gravity is witnessed by the quantum squeezing of light.

In her live Perimeter Public Lecture webcast on March 3, 2021, Priyamvada Natarajan guided the audience through what we currently know about the nature of dark matter and black holes. Natarajan is a professor in the Departments of Astronomy and Physics at Yale University, noted for her seminal contributions toward mapping the distribution of dark matter and tracing the growth history of black holes.

There has been much theorizing on the question of how the procedures of quantum theory might modify general relativity, perhaps leading to a resolution of the problem of the space-time singularities of gravitational collapse. However, I shall argue that these procedures cannot, alone, resolve the space-time singularity issue. Instead, I shall maintain that considerations of relativity, both special and general, could well provide pointers to how the major conundrum of quantum mechanics—the collapse of the wave-function—may eventually be resolved, via curious retro-active aspects of quantum and classical reality.

In this work, we introduce and study "hybrid" fracton orders, especially though a family of exactly solvable models. The hybrid fracton orders exhibit both the phenomenology of a conventional 3d topological ordered phase and a fracton phase. There are simple yet non-trivial fusion and braiding between the excitations between the two kinds. One example is the hybrid order of the Z2 topological order with the Z2 Xcube order, in which the fracton excitations fuse into the toric code charge, and in turn, the flux loop of the toric code can fuse into various lineon excitations. In the same way there is a hybrid ordered phase of Haah's code and the 3d toric code. Proliferating certain gapped excitations in these hybrid orders can drive a phase transition into either a fracton order or a conventional 3d topological phase. 

Reference. ArXiv 2102.09555

If we live in a supersymmetric world, SUSY has to be broken at some (high) scale. I will show how the presence of a SUSY-breaking hidden sector can lead to gravitational wave (GW) signals at future interferometers. I will focus on first order phase transitions that can occur along the pseudomodulus universally related to SUSY breaking. Current bounds on the superpartners are compatible with GW signals at future interferometers, while the observation of a GW signal from a SUSY-breaking hidden sector would imply superpartners within the reach of future colliders.  Along the way, I will analyze the new field theoretical features of the phase transition along the pseudomodulus direction. These allow us to pinpoint what are the necessary requirements for a SUSY-breaking hidden sector to lead to strong GW signals.

Within the next several years pulsar timing arrays (PTAs) are positioned to detect the stochastic gravitational-wave background (GWB) likely produced by the collection of inspiralling supermassive black holes binaries, and potentially constrain some exotic physics. Searches for a GWB in real PTA data rely on Markov-Chain Monte Carlo (MCMC) analyses, which are computationally demanding and not easily accessible to non-experts. In order to develop a more intuitive understanding of what PTAs may (or may not) be able to detect, we built a simple yet realistic Fisher formalism for GWB searches with PTAs. Our formalism is able to accommodate realistic noise properties of PTAs, and allows to forecast their sensitivity not only to an isotropic GWB, but also, looking ahead, to GWB anisotropies. It moreover provides a useful tool to guide and optimize real data analysis. In this talk, I will describe the basic physics behind PTAs, then the Fisher formalism, and illustrate some applications to a real-life PTA. This talk is based on arXiv:2006.14570 and 2010.13958.

Fracton models are characterized by an exponentially increasing ground state degeneracy and point excitations with constrained motion. In this talk, I will focus on a prototypical 3D fracton model -- the X-cube model -- and discuss how its ground state degeneracy can be understood from a foliation structure in the model. In particular, we show that there are hidden 2D topological layers in the 3D bulk. To calculate the ground state degeneracy, we can remove the layers until a minimal structure is reached. The ground state degeneracy comes from the combination of the degeneracy of the foliation layers and that associated with the minimal structure. We discuss explicitly how this works for X-cube model with periodic boundary condition, open boundary condition, and even in the presence of screw dislocation defects.