#operatoralgebras — Public Fediverse posts

Some of you might have noticed that for quite a number of years I got frequently distracted from my hacking by a side project that I was working on. 😂

Happily, this is now finally completely published: 🎉

https://tuprints.ulb.tu-darmstadt.de/22028/

In my thesis I present a mathematical theory to describe the inherently probabilistic dynamics of quantum systems in terms of their possible trajectories inspired by classical coding theory. 🤓

#mathematicalPhysics #quantumStochastics
#operatorAlgebras

The course is over, with a concrete construction of quantum isomorphic (but not isomorphic) graphs from binary magic square problem!

I am typing up the lecture notes, hopefully be ready before the summer break ☺️

#quantuminformation #quantumcomputing #mathematics #OperatorAlgebras

Day 25: reconstructing quantum isomorphisms from quantum automorphisms with “matrix algebra” structure (Musto-Reutter-Verdon). My secret goal from the beginning was to remove the “special symmetric” assumptions from their theory, that I managed to do in the end. The Choi-Effros product saving the day 😊

#OperatorAlgebras #mathematics #quantumcomputing #quantuminformation

Getting close to the end of the course: nonlocal games from graph isomorphism problem leads to quantum isomorphisms of graphs (Atserias-Mančinska-Roberson-Šámal-Severini-Varvitsiotis)
#quantuminformation #quantumcomputing #mathematics #OperatorAlgebras

Day 23: synchronous game structure from graph isomorphism problem, and how to get traces on universal algebras of projections

#OperatorAlgebras #quantumcomputing #mathematics #quantuminformation

Back from the break: day 22 on Hopf algebras governing quantum isomorphism of quantum graphs, and first steps into nonlocal games.

#quantuminformation #mathematics #quantumcomputing #OperatorAlgebras

Day 21 (last lecture before Easter break): compact quantum groups emerging from quantum isomorphisms of finite quantum sets.

#OperatorAlgebras #quantumcomputing #quantuminformation #mathematics #categorytheory

Wow, it’s already day 20! Today I reviewed Hilbert C*-modules to prepare for the quantum isomorphism algebras for quantum sets.

#mathematics #quantuminformation #quantumcomputing #OperatorAlgebras

Day 19: quantum isomorphisms of classical graphs, and Hopf algebraic structures behind them. We get Hopf-Galois objects (Brannan-Chirvasitu-Eifler-Harris-Paulsen-Su-Wasilewski)

#OperatorAlgebras #quantumcomputing #quantuminformation #mathematics

Day 18: getting Hopf algebra structure from quantum automorphisms of a finite set. A quantum group shows up as a universal symmetry!
#quantuminformation #mathematics #quantumcomputing #OperatorAlgebras

Day 17: quantum homomorphisms and quantum isomorphisms of quantum graphs. Now it’s getting into an uncharted territory (without δ-forms..)

#OperatorAlgebras #quantumcomputing #mathematics #quantuminformation

Day 16: concrete correspondence between two pictures of quantum graphs for the GNS model. This paves the way for non-local game of “homomorphisms” and “isomorphisms” of quantum graphs

#quantuminformation #mathematics #quantumcomputing #OperatorAlgebras

Day 10: constructing quantum channels from quantum graphs (Duan’s result from 2009). Now we are proving something ☺️
#quantumcomputing #mathematics #OperatorAlgebras #quantuminformation

Day 9: the Stinespring dilation and quantum graphs from quantum channels
#quantuminformation #OperatorAlgebras #mathematics #quantumcomputing

Day 8: one month into the course, and we are done with working out definitions of quantum graphs from different viewpoints. Next will be the connection to quantum channels!
#quantumcomputing #mathematics #OperatorAlgebras #quantuminformation

Day 7: the first technical highlight of the course, checking that the two definitions of quantum graphs agree. #quantuminformation #OperatorAlgebras #mathematics #quantumcomputing

Day 6: transforming convolution product into usual product. I don’t know how many times (generalized) Fourier transform shows up in this story. Is it just one way in disguise, or really many ways? #quantumcomputing #mathematics #OperatorAlgebras #quantuminformation

Day 5: we start working with the second way to define quantum graphs (historically the first way). Lots of bimodules, but hopefully it will pay off when we construct examples from quantum channels! #quantuminformation #OperatorAlgebras #mathematics #quantumcomputing

It is my pleasure to announce the first meeting of the regional network "Operator Algebras in the South of the UK" (https://sites.google.com/view/operatoralgebrasinthesouth), which will take place on 3rd March 2023 in Cardiff. #Mathematics #OperatorAlgebras #conference #Maths