New Paper Dance

M. Appleby, C. A. Fuchs, B. C. Stacey and H. Zhu, “Introducing the Qplex: A Novel Arena for Quantum Theory,” arXiv:1612.03234 [quant-ph] (2016).


We reconstruct quantum theory starting from the premise that, as Asher Peres remarked, “Unperformed experiments have no results.” The tools of modern quantum information theory, and in particular the symmetric informationally complete (SIC) measurements, provide a concise expression of how exactly Peres’s dictum holds true. That expression is a constraint on how the probability distributions for outcomes of different, mutually exclusive experiments mesh together, a type of constraint not foreseen in classical thinking. Taking this as our foundational principle, we show how to reconstruct the formalism of quantum theory in finite-dimensional Hilbert spaces. Along the way, we derive a condition for the existence of a $d$-dimensional SIC.

Also available through SciRate, where I have a whole profile.

Profiles in Procrastination

In ages past, biographers read the correspondence of their subjects to gain information. There was something pleasing about finding a new morsel about an old life, a letter turning up in an unexpected place. Now… Hey, I have a page on YouTube that I forgot about until today!

Insofar as the subject of any biography is a singular self, this is the same Blake Stacey as the

Someone or something else created the

page, on which I have twice as many editions as ratings. But I am not the Blake, Stacey who wrote the Boy’s Own Adventure story “The Derelict Hunters: A Thrilling Story of the Dread Sargasso Sea” (more’s the pity).

New Paper Dance

B. C. Stacey, “Geometric and Information-Theoretic Properties of the Hoggar Lines” (2016), arXiv:1609.03075 [quant-ph].

We take a tour of a set of equiangular lines in eight-dimensional Hilbert space. This structure defines an informationally complete measurement, that is, a way to represent all quantum states of three-qubit systems as probability distributions. Investigating the shape of this representation of state space yields a pattern of connections among a remarkable spread of mathematical constructions. In particular, studying the Shannon entropy of probabilistic representations of quantum states leads to an intriguing link between the questions of real and of complex equiangular lines. Furthermore, we will find relations between quantum information theory and mathematical topics like octonionic integers and the 28 bitangents to a quartic curve.

All things told, SIC-POVMs are just about the damnedest things I’ve ever studied in mathematics.

(Also listed on SciRate.)

A Frabjous, Albeit Delayed, Day

David Mermin thanked me for finding a glitch in one of his papers. I can retire now, right?

The matter concerns “Hidden variables and the two theorems of John Bell” [Reviews of Modern Physics 65, 3 (1993), pp. 803–15]. Specifically, we turn our attention to Figure 4, the famous “Mermin pentagram,” reproduced below for convenience.


The caption to this figure reads as follows:

Ten observables leading to a very economical proof of the Bell–KS theorem in a state space of eight or more dimensions. The observables are arranged in five groups of four, lying along the legs of a five-pointed star. Each observable is associated with two such groups. The observables within each of the five groups are mutually commuting, and the product of the three observables in each of the six groups is $+1$ except for the group of four along the horizontal line of the star, where the product is $-1$.

In that last sentence, “three observables in each of the six groups” should instead read “four observables in each of the five groups” (in order to agree with the diagram, and to make sense).

Glitches and goofs can happen to anybody. I’m embarrassingly prone to them myself. I also have the pesky kind of personality that is inclined to write in when I find them. This has led to a journal-article erratum once before, and now that I think about it, it provided the seeds for two papers of my own. As they say about Wolverine, being per-SNIKT-ety pays off!

(Incidentally, it took two months for this latest erratum to appear. A sensible system could have done it in as many days, but that’s scientific publishing for you.)

Daria Makes A Deal, Chapter Eight

Now and then, I see someone mocking the idea of fanfiction—typically, “Tumblr fanfic” in particular. And it’s understandable. I mean, when the canonical material rises to such heights as, um, Batman V Superman, and Tumblr can only offer Martha Kent fighting off time-travelers who come back to kill young Clark, well, is there even really a choice to make? With the “Captain America is Hydra” story arc, Marvel provides readers with the innovative and unprecedented story of Bad Guys Use Space Thing To Make Big Good Guy Bad. Seriously, for sheer inventiveness and entertainment value, how could Tumblr or AO3 even compete?


Yes, fanfiction did give the world Christian Grey. But it also gave us Will Graham and Hannibal Lecter having Christian Grey for dinner, which has to count for something.

For previous installments of Daria Makes A Deal, see the chapter index. (For my research in quantum information theory, see my recap of recent publications.)

Fair warning: I got the Granada TV Sherlock Holmes series for Christmas and have been watching a lot of that lately.


Daria noticed herself climbing a rope up towards a treehouse.

“This is odd,” she said. “I shouldn’t have nearly the upper-body strength to be doing this so easily.” She took a good look at the knotted hemp rope.

Daria tried to work her memory backwards, to see if it offered any clues about her current situation. She recalled the fracas in the hotel lobby, and then Tom and Saavik were looking at her as though she were unwell, and she was telling them that she was just tired. She remembered thinking that she could pass off any odd behavior as due to her recent discovery of her own apparent bisexuality. Which sounded plausible enough. And so she had begged off, pleading the ineffectuality of caffeine, to hide in the room where she had awoken from her dream—

It had been only a dream, but that meant nothing at all.
Continue reading Daria Makes A Deal, Chapter Eight

Spitefic: Access Denied

And now, the third installment in my Atlas Shrugged spitefic series! For the previous entries, see here and here.

Today’s vignette is inspired by a scene which so perfectly embodies an intellectually and morally bankrupt “philosophy” that it becomes viscerally repulsive. I figured that this scenario would be a better served if the cast of characters were enlarged and some substitutions made. We begin with Dagny telling the guard to let her, Hank and Francisco pass. Again, the italicized lead-in is a quotation from the original.
Continue reading Spitefic: Access Denied

Daria Makes a Deal, Chapter Seven

Fair warning: In my dubious wisdom, I have decreed that it is time for a flashback. This is where we get to see the cascading aftereffects of Jane Lane’s summer in the art colony play out in her college years. For previous installments of DMAD, see the chapter index. The escapade with Jodie Landon was recounted in Chapter Two.


The wind down Huntington Avenue is cold.

It is the Sunday before Thanksgiving, 2001.
Continue reading Daria Makes a Deal, Chapter Seven

Daria Makes a Deal Chapter Index

Present Day. Present Time.
Serial Experiments Lain

Are dolphins making self-glorifying edits on Wikipedia?
Cetacean needed, next on #SickSadWorld!

It’s thirteen years after high school, and Daria Morgendorffer is eager to turn her life around. Standing for her principles put a serious crimp in her academic career, and finding out that her fiancé was less than faithful brought a definitive end to her domestic plans. She wants to start over, but her best chance to do so is to seize an opportunity that is fantastic in all the wrong ways…

Potent Quotables, “PC Police” Edition

Here is an instance where Noam Chomsky is on point. It comes from a 1994 interview prompted by the furor over The Bell Curve.

Part of what is happening is simply a scam. The trick is to take some position that will be greatly welcomed by the powerful (say, the editors and readers of the Wall Street Journal, etc.) with no need for concern about the status of the alleged empirical grounds or the validity, or even sanity, of the arguments.

Service to power will suffice to guarantee rave reviews, massive exposure, huge sales and the other corollaries to service to power. Then, the authors pray that someone will condemn them—if not, they can invent it. At this point they can portray themselves as tortured victims of powerful forces—like Black mothers, the radicals who (as we know) run the universities, etc.

The original gets huge media exposure, and the suffering of the victims who dared to brave the Black mothers and radicals who rule the world even more so. As I say, it’s a scam, quite a comical one in fact, but one that works brilliantly in a highly conformist intellectual culture, with remarkable intellectual and moral standards.

The “political correctness” comedy has many of the same features. In fact, the remarkable issue of the New York Times Book Review that was led off by a long praise of Herrnstein–Murray had many examples of the scam: effusive praise for a book that “dared” to say the elite had merit, even notice of the “brave, heroic” book by Harold Bloom that had the courage to say that students should read Shakespeare.

One must be awe-struck in admiration of this heroism. In the intellectual culture, it is all taken quite seriously, an interesting indication of that culture’s character.

Daria Makes a Deal, Chapter Six

PREVIOUSLY, ON DARIA: Thirteen years or so after high school, Our Heroine is a washed-up academic with a series of advanced degrees, failed relationships and irregularly successful writing efforts behind her. She left her cheating boyfriend and moved back to Boston, to live with her friend Jane Lane. Jane, now running an art shop specializing in custom movie and TV props, introduced her to a social circle featuring both old and new faces. Soon, friendship got the better of caution, and Daria found herself agreeing to cosplay Edward Elric at a science-fiction and fantasy convention.

At the convention, Daria finds herself out of place, but at just the right time to be a sympathetic listener for Saavik—a clerk, aspiring actor and Tom Sloane’s girlfriend. Their night takes a turn for the fantastical when a woman from Daria’s past arrives with a business proposal… from the Sandman, Dream of the Endless.

Content note: Frank discussion of physical intimacy. On-screen portrayal thereof at maybe a soft R. Brief violence. One instance of homophobic language. Adult 4chan Man.
Continue reading Daria Makes a Deal, Chapter Six

"no matter how gifted, you alone cannot change the world"