Fermilab is literally a couple of miles from the CME datacentre in Aurora. They must have some old accelerators they aren't using.

The original Kamiokande detector is still in the ground at the Kamioka Observatory, as far as i know. Hasn't been used for science since the '80s. That's about 300 km from either Tokyo or Osaka, so you probably still need microwaves at that end.

Now you just have to think of a trade with a signal in Chicago and an instrument in Japan. The CME has Nikkei futures, but they follow the ones in Osaka. Osaka has Dow Jones futures, which presumably follow the ones in Chicago, but the volume in Osaka is pretty small. Your best best is probably FX - both Chicago and Tokyo have dollar/yen futures with good volume.

So, who is already doing this, and how long have they been doing it?

The first message sent by telegraph was supposedly "what hath God wrought?"

The first message sent by gravity wave will be "SELL 400 AMZN"

I wonder what's stopping them. How sensitive does a neutrino receiver need to be to become viable?

One thing I am most excited about is the advent of low throughput ( ~100 bps) communication with the rise of neutrino communication. The optimizations needed to use low throughput link would be interesting to see.

I think when we get into cool near sci fi stuff we'll have faster than light communication pretty soon with quantum entanglement effects, which should be way easier to wrangle than neutrinos.

Quantum entanglement cannot transmit information faster than light unless contemporary physics is very very wrong.

Neutrinos may be hard to use but they at least known to be physically possible.