Here is the very short introduction to my Habilitation (submitted in early 2022), which sheds some (metaphorical) light on some aspects of quantum theory: on going from the whole to parts, on quantum magic squares, and on shadows of infinity. The theme from the whole to the parts revolves around eight questions. The main actresses are the non-commutativity, the tensor product, positive elements and complex numbers.
Notes for a 3h crash course into quantum information for first year Physics Master students
One can imagine a quantum magic square as coming from a very weird composition of quantum measurements. Start by noting that every row (or column) of a quantum magic square defines a POVM. The weird composition rule says that one can only compose POVMs which, when stuck on top of each other, define a quantum magic square. Is this physical, in any sense? In what world would a composition like that make sense? I don't know. What we find is that this composed object has some very different properties than the individual ones. For example, it cannot be dilated to a quantum permutation matrix (whereas every POVM can be dilated to a projective measurement). That's just one way of viewing quantum magic squares.
I tried to share some of the magic of quantum theory, of magic squares and of quantum magic squares here. How beautiful is this sculpture (by Subirachs) at the Sagrada Familia? Not to speak of the Sagrada Familia itself... I should translate the article soon.
Blog contribution to Larissa Albantakis' blog Conscious(ness) realist.
Short essay on What is reality? published in La Maleta de Portbou (March 2022). You can read it in English in here.
Notes for a 1 hour crash course on "Positivity wants to break free" (Levico, July 26, 2021.)
Notes for a 1.5 hour crash course on "Computational complexity for physicists", including the solution to a seminar where we showed that the ground state energy problem of the Ising model is NP-hard.
TEDx Talk (June 2021) where I tried to explain the things that I'm trying to understand myself... PS: the talk was recorded on a stage without an audience so it made me feel like an actress :) If you watch the talk I'd be grateful if you shared your opinions / thoughts with me.
QNLP 2020. September 21, 2020.
SemSpace 2020. August 7, 2020.
Mathematical Physics Seminar at the Laboratoire de Physique Théorique, University Paul Sabatier, Toulouse, France, December 12, 2019.
An article of "Der Standard" about my work and some personal stuff, with the title "Universal systems: Why is everything so complicated?" That's a good title, I think.
An interview for "Scilog" from Alois Pumhösel on occasion of the START Prize.
Gemma De las Cuevas. Undecidability, Uncomputability, and Unpredictability Essay contest, organized by FQXi (2020).
An interview from "Inside the Perimeter", the magazine of the Perimeter Institute for Theoretical Physics.
Article on "Investigación y ciencia" (November 2016, in Spanish).