At best you could gain a 24.5ms advantage (through the earth to other side @ 12,800km versus around it at pi*6,400km).Actually quite significant in HFT terms. But: sady this is completely impossible. The weak force is not called the weak force for no reason. Neutrinos hardly interact with matter at all - that's why they can stream through 12,800 km of solid iron almost unimpeded. You would need a detector the size of…
That's absolutely untrue. Why would you need to detect all neutrinos? Even if you were capable of detecting only a quadrillionth of all neutrinos sent your way, I could send 10^20 neutrinos per second your way.
Although this project would be extremely expensive, it's absolutely possible with today's technology.