A Tale of Turing Machines, Quantum-Entangled Particles, and Operator Algebras

Henry Yuen (University of Toronto)
Richard M. Karp Distinguished Lecture Series, Spring 2020

In a recent result known as "MIP* = RE," ideas from three disparate fields of study — computational complexity theory, quantum information, and operator algebras — have come together to simultaneously resolve long-standing open problems in each field, including a 44-year old mystery in mathematics known as Connes’ Embedding Problem. In this talk, I will describe the evolution and convergence of ideas behind MIP* = RE: it starts with three landmark discoveries from the 1930s (Turing’s notion of a universal computing machine, the phenomenon of quantum entanglement, and von Neumann’s theory of operators), and ends with some of the most cutting-edge developments from theoretical computer science and quantum computing.

This talk is aimed at a general scientific audience, and will not assume any specialized background in complexity theory, quantum physics, or operator algebras.

[declup]

I've really enjoyed this presentation. My thanks to the Simons Institute and to Henry Yuen.

[avareallymeow]

This was so cool, I especially loved how the concepts were explained in a way that wasn't too technical!

[quTANum]

Such a nice talk! Many big ideas explained clearly.

[dickybannister]

That this has only been viewed like 2000 odd times is shocking. It should be a documentary. it is so good. I gravitated here via Quanta Magazine so I have a bit of background.But I think that this could easily be used to present to and inspire even non college students. You have a great style and the content is just amazing. A channel like Computerphile (the Numberphile computer channel) should be presenting this stuff to its audience via interviews and chats. Thanks again. best thing I've seen in ages

[declup]

Is there any kind of connection between the work of John Stewart Bell and that of John Lane Bell?

(I know I shouldn't expect from a coincidental sharing of names any link in the professional lives of these two men, but I've been reading some J. L. Bell lately, and there's _just_ enough commonality between physics and philosophy of math to prompt in me some daffy curiosity.)

[nullvoid]

Does these all mean that we are limited by the incompleteness posed by logician Kurt Gödel?