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Blake C. Stacey (bstacey@icosahedron.website)'s status on Wednesday, 30-Jan-2019 13:31:13 EST Blake C. Stacey

In happier* news, I was revisiting a paper my group put out last month (https://arxiv.org/abs/1812.08762) and saw how to upgrade a conjecture to a theorem.
*than whatever else is going on, probably
In conversation Wednesday, 30-Jan-2019 13:31:13 EST from icosahedron.website permalink
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  Triply Positive Matrices and Quantum Measurements Motivated by QBism
  
  from arXiv.org
  
  We study a class of quantum measurements that furnish probabilistic representations of finite-dimensional quantum theory. The Gram matrices associated with these Minimal Informationally Complete quantum measurements (MICs) exhibit a rich structure. They are "positive" matrices in three different senses, and conditions expressed in terms of them have shown that the Symmetric Informationally Complete measurements (SICs) are in some ways optimal among MICs. Here, we explore MICs more widely than before, comparing and contrasting SICs with other classes of MICs, and using Gram matrices to begin the process of mapping the territory of all MICs. Moreover, the Gram matrices of MICs turn out to be key tools for relating the probabilistic representations of quantum theory furnished by MICs to quasi-probabilistic representations, like Wigner functions, which have proven relevant for quantum computation. Finally, we pose a number of conjectures, leaving them open for future work.

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