The MINERvA experiment at Fermilab already demonstrated communication with neutrinos, admittedly over short distance: "The link achieved a decoded data rate of 0.1 bits/sec with a bit error rate of 1% over a distance of 1.035 km, including 240 m of earth."

https://arxiv.org/abs/1203.2847

Anyone from an HFT firm who wants to look into a partnership researching a neutrino link to the CME data center feel free to reach out :)

There has been a lot of progress in the past 20 years on antineutrino detection. Antineutrinos are produced by fission and so there's been a fair bit of interest in detecting them to detect covert nuclear tests as well as potentially a new modality of detecting nuclear submarines.

I think it could become possible before too long to use this to transmit data. It would probably be a ~billion dollar project, but the HFT arbitrage market is essentially winner-take-all, and may be large enough to support this size investment.

And you'd also have to ignore all the insane amounts of noise coming from regular neutrinos wizzing about in the universe.