Scientific Series

Entanglement in quantum many-body systems is typically fragile to interactions with the environment. Generic unital quantum channels, for example, have the maximally mixed state with no entanglement as their unique steady state. However, we find that for a unital quantum channel that is `strongly symmetric', i.e. it preserves a global on-site symmetry, the maximally mixed steady state in certain symmetry sectors can be highly entangled. For a given symmetry, we analyze the entanglement and correlations of the maximally mixed state in the invariant sector (MMIS), and show that the entanglement of formation and distillation are exactly computable and equal for any bipartition. For all Abelian symmetries, the MMIS is separable, and for all non-Abelian symmetries, the MMIS is entangled. Remarkably, for non-Abelian continuous symmetries described by compact semisimple Lie groups (e.g. SU(2)), the bipartite entanglement of formation for the MMIS scales logarithmically ∼logN with the number of qudits N.

I discuss how quantum mechanical effects prevent violations of causality in low energy processes, even when faster-than-light propagation is possible. At the classical level, faster-than-light propagation can be used to build "time-machine" configurations that violate causality. However, low-energy quantum excitations propagating on these backgrounds lead to divergent backreaction through loop effects. These divergences fully probe the UV dynamics of the system, making it impossible to prepare and describe causality violating configurations in the regime of validity of effective field theory. In light of these results, I conclude that effective field theories with negative Wilson coefficients or Galileon-symmetric interactions are not in tension with causality, despite leading to faster-than-light propagation.

While quantum correlations between two spacelike-separated systems are fully encoded by the bipartite density operator associated with the joint system, what operator encodes quantum correlations across space and time? I will describe the general theory of such "quantum states over time" as well as a canonical example that encodes the expectation values of certain observables measured sequentially in time. The latter extends the theory of pseudo-density matrices to arbitrary dimensions, not necessarily restricted to multi-qubit systems. In addition, quantum states over time admit a natural proposal for a general-purpose quantum Bayes' rule. Our results specialize to many well-studied examples, such as the state-update rule, the two-state vector formalism and weak values, and the Petz recovery map. This talk is based on joint work with James Fullwood and the two papers: arXiv: 2212.08088 [quant-ph] and 2405.17555 [quant-ph].

Hot viscous plasmas unavoidably emit a gravitational wave background, similar to electromagnetic black body radiation. In this talk we will discuss the contribution from hidden particles to the diffuse background emitted by the primordial plasma in the early universe. While this contribution can easily dominate over that from Standard Model particles, both are capped by a generic upper bound that makes them difficult to detect with interferometers in the foreseeable future. We will illustrate our results on the examples of axion-like particles and heavy neutral leptons. We will also discuss how this bound affects the previous estimates of gravitational wave backgrounds from particle decays out of thermal equilibrium.

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I will review various mechanisms and detection strategies of precursor emission to black holes and neutron stars mergers. I will also discuss other peculiar physical processes at the intersection of electromagnetism, classical General Relativity, and the physics of continuous media.

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Some of the most fundamental challenges in quantum gravity involve determining how to take the continuum limit of the underlying regularized theory and how to preserve the causal structure of space-time. Several approaches to quantum gravity attempt to address these questions, but the technical challenges are substantial.

In this talk, we present a novel approach to a lattice-regularized theory of quantum gravity, using techniques from standard lattice quantum field theories to overcome these challenges. Our approach is inspired by quantum geometrodynamics, the earliest attempt at quantizing gravity. While the original approach suffered from the usual shortcomings pertaining to the multiplication of distributions and consequently failed, we propose a novel lattice regularization that is especially well suited for studying the continuum limit. First, we examine the lattice corrections to the theory and quantize these lattice theories in a manner that ensures the manifest causal structure of space-time. Next, we discuss the constructions involved in obtaining a well-defined continuum limit and explain how our approach can overcome some conceptually unappealing aspects.

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Predicting the outcome of scattering processes of elementary particles in colliders is the central achievement of relativistic quantum field theory applied to the fundamental (non-gravitational) interactions of nature. While the gravitational interactions are too minuscule to be observed in the microcosm, they dominate the interactions at large scales. As such the inspiral and merger of black holes and neutron stars in our universe are now routinely observed by gravitational wave detectors. The need for high precision theory predictions of the emitted gravitational waveforms has opened a new window for the application of perturbative quantum field theory techniques to the domain of gravity. In this talk I will show how observables in the classical scattering of black holes and neutron stars can be efficiently computed in a perturbative expansion using a world-line quantum field theory; thereby combining state-of-the-art Feynman integration technology with perturbative quantum gravity. Here, the black holes or neutron stars are modelled as point particles in an effective field theory sense. Fascinatingly, the intrinsic spin of the black holes may be captured by a supersymmetric extension of the world-line theory, enabling the computation of the far field wave-form including  spin and tidal effects to highest precision. I will review our most recent results at the fifth order in the post-Minkowskian expansion amounting to the computations of hundreds of thousands of four loop Feynman integrals.

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Bayesian causal structure learning aims to learn a posterior distribution over directed acyclic graphs (DAGs), and the mechanisms that define the relationship between parent and child variables. By taking a Bayesian approach, it is possible to reason about the uncertainty of the causal model. The notion of modelling the uncertainty over models is particularly crucial for causal structure learning since the model could be unidentifiable when given only a finite amount of observational data. In this paper, we introduce a novel method to jointly learn the structure and mechanisms of the causal model using Variational Bayes, which we call Variational Bayes-DAG-GFlowNet (VBG). We extend the method of Bayesian causal structure learning using GFlowNets to learn not only the posterior distribution over the structure, but also the parameters of a linear-Gaussian model. Our results on simulated data suggest that VBG is competitive against several baselines in modelling the posterior over DAGs and mechanisms, while offering several advantages over existing methods, including the guarantee to sample acyclic graphs, and the flexibility to generalize to non-linear causal mechanisms.

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I will argue that there are quantum states of the field theories of general relativity and electromagnetism that we typically ignore, but have interesting phenomenological effects. These states amount to relaxing the constraint equations known as the Hamiltonian and momentum constraints in GR and Gauss’ law in EM. Turning off the Hamiltonian constraint sources non-dynamical parts of the metric which mimic a pressure-less dust, and thus these effects may be the explanation as to why we have inferred the existence of dark matter, both locally and cosmologically. Turning off the momentum constraints add additional velocity-dependent source terms to this effective dust, but these effects are not conserved and redshift quickly outside the horizon. Turning off the Gauss’ law constraint mimics a charge density that does not respond to electric forces, but follows geodesics, thus adding a charged component to the dust. The effects in electromagnetism may have interesting impacts on BBN, the baryon-photon fluid during and after recombination, galactic dynamics, and cosmic rays. If this new structure in the gravitational and electric fields explain dark matter, it forbids an early period of inflation and therefore requires a different explanation for density perturbations.

We develop a Machine-Learning Renormalization Group (MLRG) algorithm to explore and analyze many-body lattice models in statistical physics. Using the representation learning capability of generative modeling, MLRG automatically learns the optimal renormalization group (RG) transformations from self-generated spin configurations and formulates RG equations without human supervision. The algorithm does not focus on simulating any particular lattice model but broadly explores all possible models compatible with the internal and lattice symmetries given the on-site symmetry representation. It can uncover the RG monotone that governs the RG flow, assuming a strong form of the $c$-theorem. This enables several downstream tasks, including unsupervised classification of phases, automatic location of phase transitions or critical points, controlled estimation of critical exponents, and operator scaling dimensions. We demonstrate the MLRG method in two-dimensional lattice models with Ising symmetry and show that the algorithm correctly identifies and characterizes the Ising criticality.

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Asymptotically safe quantum gravity might provide a unified description of the fundamental dynamics of quantum gravity and matter. The realization of asymptotic safety, i.e., of scale symmetry at high energies, constraints the possible interactions and dynamics of a system. In this talk, I will first introduce the scenario of asymptotic safety for gravity with matter, and explain how it can be explored using functional methods. I will then emphasize, how the constraints on the microscopic dynamics of matter arising from quantum scale symmetry can turn into constraints on the gravitational dynamics, both by exploring the asymptotically safe fixed-point structure, and by exploring resulting infrared physics.

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