brief `category:people`

-entry for hyperlinking references

brief `category:people`

-entry for hyperlinking references

brief `category:people`

-entry for hyperlinking references

recording some reference in reply to the question: “What about quantum channels that admit an environmental representation where the environment starts out in its maximally mixed state?”

]]>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 operationis 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”

a bare list of references, to be `!include`

-ed into the references lists of relevant entries

recorded some recent surveys of the status of MOND at *MOND*

a bare minimum, for the moment just to make links work

]]>added pointer to

- Maren Justesen,
*Bikategorien af Profunktorer*, Aarhus 1968 (pdf)

(via user varkor, here)

]]>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, $f(x) = pv\left( \frac{1}{x}\right)$ is the unique distributional solution to $x f = 1$?

Added the characterization of $Comp$ as the unique non-trivial pretopos which is well-pointed, filtral and admits all set-indexed copowers of its terminal object from

- Vincenzo Marra, Luca Reggio,
*A characterisation of the category of compact Hausdorff spaces*, (arXiv:1808.09738)

Basic start for the notion introduced by Dyckerhoff and Kapranov.

]]>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*)

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.

]]>added monographs by Paul Busch to the references

and added quotes from Griffiths 2012 critiquing the idea of POVMs as “generalized measurements”

]]>brief `category:people`

-entry for hyperlinking references

brief `category:people`

-entry

following Zoran’s suggestion I added to the beginning of the Idea-section at monad a few sentences on the general idea, leading then over to the Idea with respect to algebraic theories that used to be the only idea given there.

Also added a brief stub-subsection on monads in arbitrary 2-categories. This entry deserves a bit more atention.

]]>in analogy to what I just did at classical mechanics, I have now added some basic but central content to quantum mechanics:

Quantum mechanical systems

States and observables

Spaces of states

Flows and time evolution

Still incomplete and rough. But I have to quit now.

]]>brief `category:people`

-entry for hyperlinking references

brief `category:people`

-entry for hyperlinking references

I have added (here) pointer to:

- Sergei Winitzki, Chapter 14 of:
*The Science of Functional Programming – A tutorial, with examples in Scala*(leanpub:sofp)

(This edit prompted by discussion in another thread of the same name: here)

]]>