von Neumann algebraic quantum information theory and entanglement in infinite quantum systems
Lauritz van Luijk Leibniz University Hannover
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String Theory Course Q&A
PIRSA:25050008Kinematic Stratifications
Bernd Strumfels Max Planck Institute for Mathematics in the Sciences
The Quadratic Formula Revisited
Bernd Strumfels Max Planck Institute for Mathematics in the Sciences
Axion-dilaton interactions in the dark sector
Adam Smith University of Sheffield
String Theory Course Q&A
PIRSA:25050007Neural Networks and Quantum Mechanics
Christian Ferko Northeastern University
von Neumann algebraic quantum information theory and entanglement in infinite quantum systems
Lauritz van Luijk Leibniz University Hannover
In quantum systems with infinitely many degrees of freedom, states can be infinitely entangled across a pair of subsystems. But are there different forms of infinite entanglement? In the first part of my talk, I will present a von Neumann algebraic framework for studying information-theoretic properties of infinite systems. Using this framework, we find operational tasks that distinguish different forms of infinite entanglement, and, by analysing these tasks, we show that the type classification of von Neumann algebras (types I, II, III, and their respective subtypes) is in 1-to-1 correspondence with operational entanglement properties. Our findings promote the type classification from mere algebraic bookkeeping to a classification of infinite quantum systems based on their operational entanglement properties. In the second part, I will discuss what is known about the type classification of the von Neumann algebras arising in quantum many-body systems. Together with our results, this identifies new operational properties, e.g., embezzlement of entanglement, of well-known physical models, e.g., the critical transverse-field Ising chain or suitable Levin-Wen models. Joint work with: Alexander Stottmeister, Reinhard F. Werner, and Henrik WilmingFlatness and spikes in Ponzano-Regge
The original spinfoam amplitude, Ponzano-Regge, has two properties in seeming contradiction: (1.) It can be written as an integral of a product of Dirac delta functions imposing that holonomies be exactly flat, and (2.) In its original sum-over-spins form, its leading order large spin asymptotics consist in Regge calculus, modified to include an additional local discrete orientation variable for each tetrahedron, which, when fixed inhomogeneously, leads to critical point equations for the edge lengths which do not necessarily imply flatness, but allow spikes. Of course, this apparent contradiction between flatness and spikes appears only for triangulations with bubbles, for which both of these formulations of the model are divergent and ill-defined anyway, and this may be the resolution of the paradox. However, we explore the possibility of another resolution of this paradox which may also have relevance for the semiclassical regime of 4D spinfoams, in which a similar sum over local orientations appears.
Theoretical physics at ELI ERIC
Sergey BulanovAs part of a visit to Perimeter of a delegation from the ELI Beamlines laser facility in the Czech Republic, Dr. Bulanov will speak about potential topics for collaboration between Perimeter Institute and
ELI theorists on topics related to high energy laser physics. To highlight the interplay between theory and experiment, Dr. Bulanov will briefly mention two experiments where this was realized and is currently planned at the ELI Beamlines facility.String Theory Course Q&A
PIRSA:25050008Kinematic Stratifications
Bernd Strumfels Max Planck Institute for Mathematics in the Sciences
This lecture discusses the stratification of regions in the space of real symmetric matrices. The points of these regions are Mandelstam matrices for momentum vectors in particle physics. The kinematic strata are indexed by signs and rank two matroids. Matroid strata of Lorentzian polynomials arise when all signs are nonnegative. We describe the posets of strata, for massless and massive particles, with and without momentum conservation. This is joint work with Veronica Calvo and Hadleigh Frost.
The Quadratic Formula Revisited
Bernd Strumfels Max Planck Institute for Mathematics in the Sciences
High school students learn how to express the solution of a quadratic equation in one unknown in terms of its three coefficients. Why does this formula matter? We offer an answer in terms of discriminants and data. This lecture invites the audience to a journey towards non-linear algebra.
Approximate entropy accumulation
Frédéric DupuisThe entropy accumulation theorem (EAT) allows us to lower bound the min-entropy of a state that can be generated by a chain of quantum channels satisfying a Markov chain condition, and can be used to prove the security of QKD protocols, including device-independent ones. However, one of its drawbacks is that it only applies to states with a fairly rigid structure; in particular, the Markov chain condition must be satisfied exactly. What happens when we relax this assumption by allowing the required structure to be satisfies only approximately? Does doing so lead to interesting applications? We answer both questions by the affirmative: we present two flavours of approximate EAT, and show that it can be used to prove the security of parallel device-independent QKD, and to analyze QKD protocols under source correlations. Along the way, we will introduce the concept of "approximation chain" which underpins the new results. This is joint work with Ashutosh Marwah; the talk will cover material from 2412.06723, 2402.12346, and 2308.11736.Axion-dilaton interactions in the dark sector
Adam Smith University of Sheffield
Axion-dilaton models provide a well-motivated, minimal class of models for which kinetic interactions between multiple scalar fields and their predictions can be explored, in particular in late time cosmology. I will review this class of models and present the formalism we developed for studying kinetic interactions between rapidly oscillating axion fields and their dilaton partners on cosmological scales.Self testing in General Probabilistic Theories
Lionel DmelloThis talk will consist of two parts. In the former I discuss published work [LD, Ligthart, Gross, PRA, 2024], and in the latter some new related results. Part 1 -- Although there exist theories with "stronger bipartite entanglement" than quantum mechanics (QM), in sense that they have a larger CHSH value than Tsirelson's bound for QM, all such theories known tend to come at a cost, namely, they have strictly weaker bipartite measurements. Thus it has been conjectured that if one looks at scenarios where the correlations depend both on bipartite states and bipartite measurements, e.g. entanglement swapping, such theories cannot beat QM. However, in our recent work [LD, Ligthart, Gross, PRA, 2024], we constructed a General Probabilistic Theory (GPT) -- Oblate Stabilizer Theory (OST) -- that can both achieve a CHSH value of 4 (the mathematical maximum), and maintain this CHSH value after arbitrarily many rounds of entanglement swapping, effectively ruling out this conjecture. Part 2 -- One particularly non-intuitive feature of OST (for those in the know) is the presence of a "spurious extra dimension" in the local theory: Even though the CHSH violation involves only a two-dimensional section of local state space, we failed to make the entanglement swapping property work without going to three dimensions. In ongoing work, we managed to identify the mechanism behind this phenomenon. To this end, we have introduced a notion of self-testing for GPTs, and, using this we have established a GPT version of the "no-pancake" theorem that says that there is no completely positive map that maps the Bloch sphere to a two-dimensional section. Further, under reasonable assumptions, we have also managed to establish the uniqueness of OST, and provide a prescription for the construction of GPTs capable of stable iterated entanglement swapping.String Theory Course Q&A
PIRSA:25050007Neural Networks and Quantum Mechanics
Christian Ferko Northeastern University
In this talk, I will survey recent developments about the connection between neural networks and models of quantum mechanics and quantum field theory. Previous work has shown that the neural network - Gaussian process correspondence can be interpreted as the statement that large-width neural networks share some properties with free, or weakly interacting, quantum field theories (QFTs). Here I will focus on 1d QFTs, or models of quantum mechanics, where one has greater theoretical control. For instance, under mild assumptions, one can prove that any model of a quantum particle admits a representation as a neural network. Cherished features of quantum mechanics, such as uncertainty relations, emerge from specific architectural choices that are made to satisfy the axioms of quantum theory. Based on 2504.05462 with Jim Halverson.