The MUB Project

 I will be updating this post regarding my project work. All the orange words are links!

1) Initial report 

2) MASAs and MUBs - Part 1 (edited) This report isn't complete or self contained but it is my summary of the sections of Andras Szanto's paper [here] that I found relevant to the problem. There is no original contribution from my end in either this or the previous writeup, they are only meant to clarify terminology and set the stage.

Some large updates coming soon! (1 Jan 2023)

Said update :

I am about 11 months late to post this, but attached below is some code (in MATLAB. I am truly sorry, some array operations are just way more convenient here) I wrote to show, essentially by brute force, that all classes of weakly unextendible MASAs belong to a complementary decomposition that satisfies Szanto's criterion. See this report explaining that monstrosity of a program and some interesting findings. I hope to actually improve the speed of this program and therefore execute it for p=5 too, at least.

Step 1 - Initialize

Step 2 - Find Factors

Step 3 - Exclude Extendible MASAs

Step 4 - List of complementary decompositions

The conjecture on allowable factors - Only stores factor lists obeying the condition, that any element of one factor commutes with every element of another factor

A further check - After step 2, you could exclude factors whose elements can be reshuffled into a set of MASAs, as those cannot arise in any complementary decomposition obeying Szanto's criterion. 

Put each step into a separate .m files and save them in the same directory if you want to test it out for yourself. I hope I will be able to redo this in C++ and clean it up.