I worked on an example for the Antidistinguishability Threshold for Equiangular States and made a
Pull Request on the 4th of July. This example shows how we can numerically verify a tight bound presented in the paper
"Tight bounds for antidistinguishability and circulant sets of pure quantum state" by Johnston et. al and visualize the “sharp cliff” where this property changes. I would like to mention that I really enjoyed reading this paper as it powerfully analyzes the concept of "antidistinguishability", which is very important to the PBR proof. It's beautiful how this paper makes it simple to check if states are "antidistinguishable" by showing it only depends on the mathematical overlaps between the states, not on finding a complex quantum measurement. I recommend!
Anyway, I realized that in the description of the
GitHub Issue I had opened earlier, I mistakenly wrote that we could use the
vector_to_gram_matrix.py function from |toqito⟩ for this example. I have explained in the pull request description that it was in the wrong direction.
This
Pull Request is for another example based on the same paper, which shows how we can numerically verify a powerful necessary and sufficient condition based on the eigenvalues of the states’ Gram matrix, as presented in the paper. This is a very important result from the paper (Theorem 5.1). In the "furthermore" part, the proof is a beautiful chain of equivalences using the concept of dual cones. More reasons to appreciate the paper! As usual, I will refine both PRs based on my mentors' feedback.