Connes Embedding Problem: MIP* = RE"

[.Scott]

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.

 

[Future Bruno]

The conjecture asks whether every von Neumann algebra can be embedded into a larger von Neumann algebra in such a way that the original algebra’s structure is preserved.The proof shows that the Connes Embedding Problem (CEP) is computable when quantum information is exchanged among many provers. This means that CEP admits a polynomial-time algorithm when quantum information is exchanged among many provers. The result also implies that CEP can be computed using a protocol of communication complexity (always assuming quantum information exchange). This implies that CEP is solvable in polynomial time when quantum information is exchanged among many provers.The paper also provides a framework for constructing protocols for solving the Interrogator problem in polynomial time when quantum information is exchanged among many provers. This result has implications for quantum computing, where it may enable more efficient algorithms for solving certain problems. In addition, the paper provides insight into other problems related to quantum computing and mathematics, such as the Quantum Entanglement Games.

 

[Future Bruno]

In this paper, we prove that the Interrogator problem is computable when quantum information is exchanged among the Many Provers. This result resolves the Connes Embedding Problem, and implies that the problem can be solved in polynomial time. We also show that this result has implications for the development of quantum computing and the study of quantum information theory.