Motivated by other blogs presenting scientific knowledge from different areas, we have decided to start our own blog on* incompatibility.* Specifically, we would like to dwell especially in the world of quantum incompatibility, which is something we like and something that bears a lot of interest for us. Yes, we like quantum, because it is something what our intuition is not trained for. So in this blog we will make (and host) posts that will illustrate and hopefully also explain the effects of quantum theory that are harder to grasp. The plan is to make posts both on general knowledge in the theory and more specific new (smaller or bigger) results, possibly supplemented by examples to help digest them.

In this first blog post let us tell you something about the topic in some broader term, namely, what is compatibility? It is exactly what the name suggests: it is the idea that two or more things can “work together”. Take for example following shadows:

As the picture shows, the three shadows come from a single object, although it takes a bit of thinking to decide whether it is so when only the shadows are available.

In the same way we ask a multitude of questions about compatibility of other different devices: a flat-head screwdriver is incompatible with a hex socket screw; tea and milk can be put together and make a good drink, and as such they seem to be compatible (I (Daniel) tested it on my taste buds, but would argue otherwise); and Slovak institutions do not offer good services, and so are also incompatible. These are everyday compatibility problems that arise, but there are many more hidden in the quantum realm and those provide questions we are interested in.

In the following posts we will try to dig deeper into these quantum questions and provide answers where we know them. We hope you will enjoy reading this blog as much as we will writing it.

Daniel and Teiko

(Many thanks to Tom Bullock for proof-reading)

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Hi,

I am looking forward to interesting blog posts. The picture reminded me of a nice riddle:

Is there a simply connected curve in 3-dimensional space such that any of the 3 shadows (as you depicted it), i.e. any of the projections to the planes with x_k=0 for k=1,2,3 , is a tree, i.e. a connected cycle-free graph ?

Have fun!

Alexander

Of course I meant simply closed instead of simply connected.

Yes, this I understood. But so far, I have not found any example. Is there such curve?

http://www.amazon.com/Mathematical-Mind-Benders-Peter-Winkler-ebook/dp/B0049P1YWA