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I added some simpler motivation in terms of the basic example to the beginning of distributive law.
started a still highly stubby entry on nonabelian Hodge theory.
So far all I have is some references and the statement of "Corlette's theorem".
created Hodge structure. Currently with nothing but a pointer to this nice book:
Eventually I’d think we should move over Hodge-structure articles from Hodge theory to here. But not tonight.
I have tried to brush-up Kleisli category; also made Kleisli composition redirect to it and cross-linked with monad (in computer science)
added monographs by Paul Busch to the references
and added quotes from Griffiths 2012 critiquing the idea of POVMs as “generalized measurements”
now creating this entry.
The technical material under “Details” (here) is copied over from what I had written at reader monad – Examples – quantum reader monad. (There may still be room left to adjust the wording in order to reflect that this material moved to a new entry.)
To this I have now added an Idea-section (here) which highlights the relation to (equivalence with) Bob Coecke’s “classical structures” (which term I made redirect to here now)
Starting an entry (to rhyme on “quantum reader monad”) on the linear version of the costate comonad and how its coKleisli category on the tensor unit alone exhibits the structure of quantum observables.
Am starting a write-up (here) of how (programming languages for) quantum circuits “with classical control and/by measurement” have a rather natural and elegant formulation within the linear homotopy type theory of Riley 2022.
Aspects of this have a resemblance to some constructions considered in/with “Quipper”, but maybe it helps clarify some issues there, such as that of “dynamic lifting”.
The entry is currently written without TOC and without Idea-section etc, but rather as a single top-level section that could be !include
-ed into relevant entries (such as at quantum circuit and at dependent linear type theory). But for the moment I haven’t included it anywhere yet, and maybe I’ll eventually change my mind about it.
Minimal person entry on a Slovenian mathematician, his formula plays major role in the entry principal value.
I want to be adding some details to Cauchy principal value. What’s a good reference? Say for the proof that up to addition of a delta-distribution, is the unique distributional solution to ?
Stub for triple category.
Adding reference
Anonymouse
edited dualizable object a little, added a brief paragraph on dualizable objects in symmetric monoidal -categories
Added a literature reference to icon. Started some systematic notes on icons for monoidal-enriched bicategories, which I am currently using for something. Think the broken-off state of that section is not intolerable, in particular since I have seen similar work in progress on the nLab. Intend to continue them soon.
I added a section on strictification of pseudofunctors to pseudofunctor, after seeing Finn and Mike respond to Karol in the stable monoidal derivator thread at the Café. The discussion is fairly sketchy and pedestrian. Also added a few references.
Wikipedia has a nice article on quantum operations.
The nLab also had a page quantum operations and channels (cache bug?), but I’ve renamed this to simply quantum operation since a quantum channel seems to be nothing but a quantum operation when viewed from the perspective of quantum information theory. Eventually, this page might need some disambiguation since there may be several uses of the term, but for now I think it is “ok”.
I think this page can be cleaned up. I started, but don’t think I will be able to finish.
In particular, there is some background material that might be better on separate pages. I’ll continue trying to clean things up, but family might be calling soon and I’ll need to run quickly whatever state it is in.
I also made the simple statement
In quantum mechanics, a quantum operation is a morphism in the category of density matrices
at the beginning of the Idea section motivated by O’Loan’s comment
A quantum channel is a mapping which sends density matrices to density matrices.
This seems innocent enough, but someone might check the statement. For one, I’ve never seen a category of density matrices, but the idea seems obvious enough. Maybe a word on density matrix would be good.
this is a bare sub-section — meant to be !include
ed into relevant entries such as at quantum channel and at quantum decoherence — towards the theorem that quantum channels are exactly the “bath-averages of bath-coupled unitary evolutions”
recorded some recent surveys of the status of MOND at MOND
Added the characterization of as the unique non-trivial pretopos which is well-pointed, filtral and admits all set-indexed copowers of its terminal object from
starting a bare minimum, to make links work.
(The single example included is copied over from revision 1 of partial trace, where I had deleted it as announced there. It needs attention, if only for the typesetting).
a bare sub-section, to be !include
-ed into relevant entries (such as at quantum measurement channel)