Tuesday, April 21, 2020

The proof

Zhengfeng JiAnand NatarajanThomas VidickJohn WrightHenry Yuen
We show that the class MIP* of languages that can be decided by a classical verifier interacting with multiple all-powerful quantum provers sharing entanglement is equal to the class RE of recursively enumerable languages. Our proof builds upon the quantum low-degree test of (Natarajan and Vidick, FOCS 2018) by integrating recent developments from (Natarajan and Wright, FOCS 2019) and combining them with the recursive compression framework of (Fitzsimons et al., STOC 2019).
An immediate byproduct of our result is that there is an efficient reduction from the Halting Problem to the problem of deciding whether a two-player nonlocal game has entangled value 1 or at most 12. Using a known connection, undecidability of the entangled value implies a negative answer to Tsirelson's problem: we show, by providing an explicit example, that the closure Cqa of the set of quantum tensor product correlations is strictly included in the set Cqc of quantum commuting correlations. Following work of (Fritz, Rev. Math. Phys. 2012) and (Junge et al., J. Math. Phys. 2011) our results provide a refutation of Connes' embedding conjecture from the theory of von Neumann algebras.

It can be simplified, proof the unique existence of a Dophantine for any dimension.  Then show the validator will converge only when N set set to its dimensional constant. Evidently the Dophantine proof can be used across a wide variety of problems, as I have shown. There should be a Markov tree for any dimension. The remaining issue is the existence of an orthogonalizing transformation that takes the N dimensional system and makes an N+1 dimensional system with scaled axis, the relativity problem. And that should exist is my conjecture, that is the abstract problem.

For any N dimensional Chinese remainder problem, or the optimum number of elements needed to pack an N dimensional sphere or when will an N coloring problem converge. What is the reductions algorithm for a factorial graph. All those problems collapse into the proof of existence for a Dolphantine.

They method creates a sequence of error qubits. They count error updates as 1/2,1/3,1/5,1/7 and so on, depending on the dimension. The rank of the error matrix equal to the dimensionaliy. The error channel is maximally white so each of the error bits has the same probability of firing, thus they are independent events.  The system has removed all redundancy in the error graph which is minimal spanning tree without loops after the thinning.

So, yes there is a theory of every thing and no, I am not getting a job, thanks anyway.

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