Scientific Series

Aaronson and Ambainis (2009) and Chailloux (2018) showed that fully symmetric (partial) functions do not admit exponential quantum query speedups. This raises a natural question: how symmetric must a function be before it cannot exhibit a large quantum speedup? In this work, we prove that hypergraph symmetries in the adjacency matrix model allow at most a polynomial separation between randomized and quantum query complexities. We also show that, remarkably, permutation groups constructed out of these symmetries are essentially the only permutation groups that prevent super-polynomial quantum speedups. We prove this by fully characterizing the primitive permutation groups that allow super-polynomial quantum speedups. In contrast, in the adjacency list model for bounded-degree graphs (where graph symmetry is manifested differently), we exhibit a property testing problem that shows an exponential quantum speedup. These results resolve open questions posed by Ambainis, Childs, and Liu (2010) and Montanaro and de Wolf (2013). Based on: arxiv:2006.12760

In recent years, it has become increasingly well-known that nearly all the major no-go theorems in quantum foundations can be circumvented by violating a single assumption: the hidden variables (that determine the outcomes) are uncorrelated with the measurement settings. A hidden-variable theory that violates this assumption can be local, separable, non-contextual and have an epistemic quantum state. Such a theory would be particularly well-suited to relativistic contexts. Are such theories actually feasible? In this talk, we discuss some results on the two physical options to violate this assumption: superdeterminism and retrocausality. 

Developing an intuitive criticism by Bell, we show that superdeterministic models are conspiratorial in a mathematically well-defined sense in two separate ways. In the first approach, we use the concept of quantum nonequilibrium to show that superdeterministic models require finetuning so that the measurement statistics do not depend on the details of how the measurement settings are chosen. In the second approach, we show (without using quantum non-equilibrium) that an arbitrarily large amount of superdeterministic correlation is needed for such models to be consistent. Along the way, we discuss an apparent paradox involving nonlocal signalling in a local superdeterministic model. 

Next, we use retrocausality to build a local, separable, psi-epistemic hidden-variable model of Bell correlations with pilot-waves in physical space. We generalise the model to describe a relativistic Bell scenario where one of the wings experiences time-dilation effects. We show, by discussing the difficulties faced by other hidden-variable approaches in describing this scenario, that the relativistic properties of the model play an important role here (otherwise ornamental in the standard Bell scenario). We also discuss the technical difficulties in applying quantum field theory to recover the model's predictions.

The Event Horizon Telescope is a global effort to construct an
Earth-sized virtual radio telescope array, with the goal to make pictures and
movies of two nearby supermassive black holes. A detailed theoretical
understanding of black hole accretion is now crucial to interpret these
observations. I will review our current efforts to model polarimetric
properties of light produced in synchrotron processes in plasma falling
towards the event horizon. The numerical models are based on general
relativistic magnetohydrodynamics simulations so they are capable of capturing
the complex dynamics of magnetic fields and their interactions with plasma. It is now
important to understand the polarized radiative transfer in these simulations
to correctly predict the observational signatures of the events at the event
horizon scales where the accretion disk and jet are connected.

In this talk, I will discuss two problems: quantum data compression
and quantum causal order discovery, both for multipartite quantum
systems. For data compression, we model finitely correlated states as
tensor networks, and design quantum compression algorithms. We first
establish an upper bound on the amount of memory needed to store an
arbitrary state from a given state family. The bound is determined by
the minimum cut of a suitable flow network, and is related to the flow
of information from the manifold of parameters that specify the states
to the physical systems in which the states are embodied. We then
provide a compression algorithm for general state families, and show
that the algorithm runs in polynomial time for matrix product states.

For quantum causal order discovery, we develop the first efficient
quantum causal order discovery algorithm with polynomial black-box
queries with respect to the number of systems. We model the causal
order with quantum combs, and our algorithm outputs the order of
inputs and outputs that the given process is compatible with. Our
method guarantees a polynomial running time for quantum combs with a
low Kraus rank, namely processes with low noise and little information
loss. For special cases where the causal order can be inferred from
local observations, we also propose algorithms that have lower query
complexity and only require local state preparation and local
measurements. Our results will provide efficient ways to detect and
optimize available transmission paths in quantum communication
networks, as well as methods to verify quantum circuits and to
discover the latent structure of multipartite quantum systems.

The Dark Energy Survey (DES) is a photometric galaxy survey which, using measurements of distortions to galaxy shapes from weak gravitational lensing and other observables, we can use to test the validity of our standard cosmological model, LambdaCDM. As an example of this, I will motivate and discuss a recent analysis of the DES Year 1 data (described in https://arxiv.org/abs/2010.05924) in which we use a "growth-geometry split" parameterization to check the consistency of constraints from structure growth and expansion history. I will also highlight some of the ongoing work on the DES Year 3 analysis, as well as challenges we will face as we subject LambdaCDM to increasingly precise tests with future cosmological experiments.

Dilaton-gravity models are integrable in two dimensions and admit a holographic description. In this talk, the holographic description of the Dilaton-gravity in flat spacetime is discussed. Using the gauge theory formulation of the model we obtain the boundary action which under certain boundary conditions is of the Warped-Schwarzian type. We calculate the 1-loop partition function of the model as the coadjoint orbit of the warped Virasoro group.

In the conventional weakly-interacting massive particle (WIMP) paradigm the late-time density of dark matter (DM) is set by the rate of two-body annihilations, but there has been considerable recent interest in exploring alternative DM scenarios where other interactions control the final abundance. I will show that by fully exploring the parameter space of a simple, weakly-coupled dark sector, we can find a rich set of novel pathways which lead to the observed relic density of DM. In particular, we can identify and characterize a general class of mechanisms in which the DM relic abundance is determined by processes controlling the thermal coupling of the DM and Standard Model (dubbed the KINetically DEcoupling Relic -- KINDER), generalizing previously-studied special cases of this behavior.

Torsion is a popular ingredient in gravity, yet fraught with quantum and classical pathologies. I develop a novel torsion theory, consistent with power-counting and unitarity. The Friedmann equations emerge (with dark energy and radiation), as do pp waves and the Schwarzschild vacuum, all without an Einstein-Hilbert term. I show that cosmology sees torsion as a non-canonical scalar, revealing a rich phenomenology of conformal or waterfall inflatons, and cuscutons. I finally argue that future work will be driven less by toy-models, and more by computer surveys. I advocate Hamiltonian and effective field theory approaches to non-Riemannian geometry in general, relevant to ultraviolet completion and modified gravity alike. Such methods should be oriented towards the ultimate test of gravity: observed cosmological structure.

A many-body quantum system that is continually monitored by an external observer may be in distinct dynamical phases, depending on whether or not the observer’s repeated local measurements prevent the buildup of long-range entanglement. The universal properties of the “measurement phase transitions” between these phases remain a challenge. In this talk I will describe new theoretical approaches to measurement phase transitions, making connections with problems in statistical mechanics such as disordered magnets and travelling waves. I will show that exact results are possible in some regimes, including for quantum circuits with all-to-all interactions. (Based on arxiv:2009.11311)

The quantum states of matter in the immediate vicinity of a black hole can be studied using no other information than Standard Model physics combined with perturbative gravity. The point is that the relevant energy scale of the most important fields involved is low compared to the Planck scale, provided the black hole is big compared to the Planck scale. Usually this problem is investigated by using the metric that includes the effects of matter that formed the black hole in the distant past and sometimes also matter that is radiated away in the distant future.  Arguments are presented however to justify that one should ignore those effects. The metric then becomes invariant under  time translation, and this is what we need to get the energy eigen states. It is this scheme that forces us to impose the antipodal identification as a new boundary condition, giving us a beautiful picture of black hole quantum evolution. The logic of choosing this compulsory topological twist in space-time is explained. There are still many very hard questions and I hope to be able to inspire people to look into these.

We introduce the notions of (G,q)-opers and Miura (G,q)-opers, where G is a simply-connected complex simple Lie group, and prove some general results about their structure. We then establish a one-to-one correspondence between the set of (G,q)-opers of a certain kind and the set of nondegenerate solutions of a system of XXZ Bethe Ansatz equations. This can be viewed as a generalization of the so-called quantum/classical duality which I studied with D. Gaiotto several years ago. q-Opers generalize classical side, while on the quantum side we have more general XXZ Bethe Ansatz equations. The generalization goes beyond the scope of physics of N=2 supersymmetric gauge theories.

In compact astrophysical objects, such as neutron star magnetospheres, black-hole accretion disk coronae and jets, the main energy reservoir is the magnetic field. The plasma processes such as magnetic reconnection and turbulence govern the extraction of that energy, which is then deposited into heat and accelerated particles and, ultimately, the observed emission. To understand what we observe, we first need to describe from first principles how these processes operate in violent regimes applicable to certain classes of compact objects, where radiative drag and pair production/annihilation play a significant role. As a specific example, I will briefly cover our state-of-the-art understanding of one of these processes — magnetic reconnection — and present the first self-consistent simulations of QED-mediated reconnection in application to neutron star magnetospheres and explain how it helps us understand the observed gamma-ray emission from these objects. I will also talk about the future prospects of this area of research; QED-mediated plasma processes also take place in a variety of other astrophysical objects, such as the accretion disk coronae in X-ray binaries, coalescing neutron stars shortly before their merger, and short X-ray bursts in magnetars.