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, called The Lovers, 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.
A 1.5 hour crash course on some of the basic ingredients on quantum information. Given to first semester Master students at the University of Innsbruck in the framework of the Lecture "Modern Physics".
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.
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).