Connes Embedding Problem: MIP* = RE"

Thread starter .Scott
Start date Aug 15, 2020

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The discussion centers on the computability of the Interrogator problem within the context of quantum information and its implications for computer science. A significant finding is that the Interrogator problem is computable when quantum information is exchanged among multiple provers. The proof, detailed in a 165-page document titled "MIP* = RE," has been pre-published and featured in Quanta Magazine. This work also addresses the Connes Embedding Problem, demonstrating that the conjecture is false. The Connes Embedding Problem, a longstanding issue in von Neumann algebra theory, has connections to quantum theory and computer science, particularly through its implications for the existence of microstates and results in von Neumann algebras.

Aug 15, 2020

.Scott

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TL;DR Summary: A paper just published in Quanta Magazine demonstrates that the Interrogator problem is computable when quantum information is exchanged among the Many Provers.

This bears on QM and pure Math - but it is fundamentally about computability - so I am posting it here in Computer Science.

The result is: The Interrogator problem is computable when quantum information is exchanged among the Many Provers.

The raw 165-page proof is pre-published here: MIP* = RE
It has been published in Quanta Magazine here: Quanta Magazine Article

The paper provides a proof to the Connes Embedding Problem (proving that the conjecture is impossible, false) and is described in the wiki article as follows:

Connes' embedding problem, formulated by Alain Connes in the 1970s, is a major problem in von Neumann algebra theory. During that time, the problem was reformulated in several different areas of mathematics. Dan Voiculescu developing his free entropy theory found that Connes’ embedding problem is related to the existence of microstates. Some results of von Neumann algebras theory can be obtained assuming positive solution to the problem. The problem is connected to some basic questions in quantum theory, which led to the realization that it also has important implications in computer science.

Last edited: Aug 15, 2020

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