Blake Stacey

Blake Staceyblake-stacey

Aug 15 2017 16:09 UTC
Jul 11 2017 16:27 UTC
Blake Stacey commented on Fibonacci-Lucas SIC-POVMs

Eight hundred forty-four!

Jul 11 2017 16:27 UTC
Blake Stacey scited Fibonacci-Lucas SIC-POVMs
Jun 15 2017 17:29 UTC
Jun 14 2017 03:30 UTC
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May 19 2017 21:48 UTC
May 12 2017 02:00 UTC
In earlier work, my colleagues and I developed a formalism for using information theory to understand scales of organization and structure in multi-component systems. One prominent theme of that work was that the structure of a system cannot always be decomposed into pairwise relationships. In this brief communication, I refine that formalism to address recent examples which bring out that theme in a novel and subtle way. After summarizing key points of earlier papers, I introduce the crucial new concept of an ancilla component, and I apply this refinement of our formalism to illustrative examples. The goals of this brief communication are, first, to show how a simple scheme for constructing ancillae can be useful in bringing out subtleties of structure, and second, to compare this scheme with another recent proposal in the same genre.
May 11 2017 03:15 UTC
Apr 19 2017 00:19 UTC
Apr 15 2017 18:13 UTC
Apr 14 2017 00:35 UTC

I agree with Steve Flammia's comment. The field norm is a nice generalization of the standard norm. (I haven't yet thought about whether there might be a physics motivation for it, rather than a purely mathematical one, but that's not important right now.) To avoid confusion, some phrase like "equiangular with respect to the field norm" or "field-norm equiangular" should be used.

Apr 12 2017 18:20 UTC

This is why I am confused (it is probably just a reading comprehension error on my part): If the POVM is IC, it must have at least $d^2$ elements. If it is a minimal IC-POVM, it must have exactly $d^2$ elements. But if it is minimal, IC and equiangular, then the angle is fixed by the requirement that the elements sum to the identity. Suppose that the trace of $\Pi_i \Pi_j$ is $\alpha$ whenever $i \neq j$. Summing this over all $j$ yields $1 + (d^2-1)\alpha$. But the projectors $\Pi_i$ themselves must sum to $dI$, so the value of $\alpha$ is fixed to $1/(d+1)$.

Apr 12 2017 00:34 UTC

Clarification request: Are all the IC-POVMs in this paper minimal? That is, does the number of elements in each POVM equal the square of the dimension? If so, I am confused about the quoted value of the inner product between projectors for the equiangular IC-POVM in dimension 5.